Students often refer to SSLC Maths Textbook Solutions and Class 10 Maths Chapter 7 Coordinates Important Extra Questions and Answers Kerala State Syllabus to clear their doubts.
SSLC Maths Chapter 7 Coordinates Important Questions and Answers
Coordinates Class 10 Extra Questions Kerala Syllabus
Coordinates Class 10 Kerala Syllabus Extra Questions
Question 1.
Which of the following is a point on y axis
(a) (1, 1)
(b) (0, -3)
(c) (-3, 0)
(d) (3, 2)
Answer:
(0, -3)
Question 2.
The line passing through (0,3) parallel to x axis and the line passing through (4, 0) parallel to y axis meet at P. What are the cordinates of P
(a) (3, 4)
(b) (4, 3)
(c) (-3, 4)
(d) (3, -4)
Answer:
(b) (4, 3)
Question 3.
A(4, 0), B(0, 4), C(-4, 0), D(0, -4) are the vertices of a quadrilateral.
a) Draw co-ordinate axes and mark the points and suggest a suitable name to ABCD
b) What is the area of ABCD?
Answer:
a) Square
b) (4√2)2 = 16 × 2 = 32 sq. units
Question 4.
(3,4) is a point on a circle with center at the origin.
a) What is the radius of the circle?
b) What are the points where the circle cut the axes?
Answer:
a) r = \(\sqrt{3^2+4^2}=\sqrt{25}\) = 5
b) (5, 0) (0, 5) (-5, 0) (0, -5)
Question 5.
A(3, 4), B(-3, 4), C(-3, -4), D(3, -4) are vertices of a rectangle .
a) Find the length of the sides
b) What is the area of ABCD?
Answer:
a) AB = |3 – (-3)| = 6, BC = 8
b) Area = 6 × 8 = 48 sq. units
Question 6.
In the figure O is the origin of coordinates and ABCD is a square. ∠AOD = 45°. If OD = \(\sqrt{18}\) then
a) Write the coordinates of the vertices of the square ABCD
b) What is the area of ABCD?
Answer:
a) OA = \(\frac{\sqrt{18}}{\sqrt{2}}\) = 3
A(3, 0), B(6, 0) ,C(6, 3), D(3, 3)
b) 32 = 9 sq. units
Question 7.
A(3, 2) B(9, 2)and C(5, 7)are the vertices of a triangle.
a) What is the length of the side parallel to x axis
b) What is the altitude to that side?
c) Calculate the area of triangle ABC
Answer:
a) |9 – 3| = 6
b) |7 – 2| = 5
c) \(\frac{1}{2}\) × 6 × 5 = 15 sq. units
Question 8.
P(6,8) is a point on a circle with center at the origin.Q is a point on the circle such that OQ makes angle 30° with x axis as in the figure
a) What is the radius of the circle?
b) What are the points where the circle cut the axes?
c) Write the coordinates of Q
Answer:
a) \(\sqrt{6^2+8^2}\) = 10
b) (10, 0), (0, 10), (-10, 0), (0, -10)
c) Draw perpendicular from Q to x axis. It is QA Triangle QAO is a 30 – 60 – 90 right triangle. Q(-5√3, 5)
Question 9.
∆ABC is an equilateral triangle. A(2, 2), B(6,2)
a) Find the length of the side.
b) Calculate the altitude to the side
c) Write the coordinates of C
d) Calculate the area of the triangle
Answer:
a) AB = |6 – 2| = 4
b) 2√3
c) Draw CP perpendicular to AB .Triangle CPA is a 30 – 60 – 90 triangle, P(4, 0)
Coordinatesof C are(4, 2 + 2√3 )
d) \(\frac{1}{2}\) × 4 × 2√3 = 4√3 Sq. units
Question 10.
Draw coordinate axes and mark the point A(-2, -2).
a) Move 4 unit parallel to y axis in the positive direction and mark the coordinates of B.
b) Move 6 unit to the right from B parallel to x axis and mark C with the coordinates.
c) Move 4 unit parallel to y axis up and mark D with its coordinates.
d) Find the distance AD
Answer:
Draw coordinate axes and mark the points
a) B(-2, 2)
b) C(4, 2)
c) D(4, 6)
d) Distance between A(-2, -2) and D(4, 6) is AD
AD = \(\sqrt{(-2-4)^2+(-2-6)^2}=\sqrt{36+64}\) = 10
Question 11.
The distance between the points (3, -5) and (5, -1) is
(a) 2√5
(b) 3√5
(c) 6√5
(d) √5
Answer:
Distance = \(\sqrt{(5-3)^2+\left(-1-^{-} 5\right)^2}\)
= \(\sqrt{2^2+4^2}\)
= \(\sqrt{20}\)
= 2√5
Question 12.
The distance between the points P( 1 ,-2)and Q (a, 1) is 5. Which of the following is one of the values of a
(a) -3
(b) 7
(c) 1
(d) 9
Answer:
\(\sqrt{(a-1)^2+\left(1-^{-} 2\right)^2}\) = 5
Squaring on both sides,
(a – 1)2 + 32 = 25,
(a – 1)2 = 25 – 9 = 16,
a – 1 = 4, -4
if a – 1 = -4, a = -3
Question 13.
P is a point on y axis. Two other points are A (13, 2) and B(12, -3). If PA = PB then
a) What is the x coordinate of P?
b) Find the co-ordinates of P?
Answer:
a) 0
b)(0, 2)
Question 14.
A(2, 3), B(3, 4)and C(4, 5) are three points on a plane
a) Find the distances AB, BC and AC
b) Are these points on a line? How can you realize?
Answer:
a) AB = √2, BC = √2, AC = 2√2
b) Since AB + BC = AC we can say A,B,C are on a line.
Question 15.
Consider the points A(2, 4), B(6, 8) and C(2, 8)
a) Find the length of the sides of triangle ABC
b) What kind of triangle is this?
Answer:
a) AC = 4, BC = 4, AB = 4√2
b) Since the sides are in the ratio 1: 1. √2 we can say it is a 45° -45° -90° triangle. It is an isosceles right triangle.
Question 16.
ABCD is a square in which one pair the opposite vertices are A(3, 4) and B(5, 6)
a) Find the length of the diagonal
b) What is the area of the square?
Answer:
a) AC = \(\sqrt{(5-3)^2+(6-4)^2}\) = 2√2
b) Area = \(\frac{1}{2}\) × AC2
= \(\frac{1}{2}\) × (2√2)2
= \(\frac{8}{2}\)
= 4 sq.units
Question 17.
Draw the coordinates axes and mark the points on the plane
a) A(1, 0), 5(6, 0), C(8, 3) and D(3, 3)
b) Write the most suitable name to ABCD
c) Calculate the area of ABCD
Answer:
a) Mark the points using co-ordinate axes.
b) Parallelogram
c) 5 × 3 = 15 sq. units
Question 18.
A circle with center at the origin cut y axis at (0, 5)
a) Write the coordinates of other three points on this circle
b) What is the radius of this circle?
c) Verify that (4, 4) is a point on this circle
Answer:
a) (0, -5), (5, 0), (-5, 0)
b) 5
c) Distance between (0, 0) to (4, 4) is (c) (12, 4)
Question 19.
ABCD is a parallelogram. A(1, 1), .8(7, 1)andC(1, 4)
a) What is the length of the side parallel to x axis ?
b) Find the length of other side
c) Find the coordinates of the vertex D
d) Calculate the area of the parallelogram.
Answer:
a) AB = |7 – 1| = 6
b) BC = \(\sqrt{(1-7)^2+(4-1)^2}\)
= \(\sqrt{36+9}=\sqrt{45}\)
= 3√5
c) D(-5, 4)
d) Distance between the parallel sides AB and CD is 4 – 1 = 3
Area = 6 × 3 = 18 sq. units
Question 20.
A(-4, -3), B(4, -3), C(7, 5), D(-7, 5) are the vertices of a quadrilateral
a) Observing the coordinates of the vertices sug-gest a suitable name to ABCD
b) Find the length of its parallel sides
c) What is the distance between the parallel sides?
d) Calculate the area of ABCD
Answer:
a) AB and CD are parallel to x axis. So these are parallel sides.Other two sides BC and AD are not parallel.
ABCD is an isosceles trapezium.
b) 4B = |4 – 4| = 8, CD = |7 – (-)7| = 14
c) Distance between the parallel sides is |5 – (-) 3| = 8
= \(\frac{1}{2}\) × h × (a + b)
= \(\frac{1}{2}\) × 8 × (8 + 14)
= 88 Sq. units
Question 21.
What is the distance between the points (-1, 7) and (8, 7)
(a) 4
(b) 9
(c) 10
(d) 8
Answer:
|8 – (-) 1| = 9
Question 22.
Center of a circle is (3,4) and radius 5. Which of the following is a point on this circle?
(a) (3, 3)
(b) (8, 1)
(c) (12, 4)
(d) (0, 0)
Answer:
(0, 0)
Question 23.
In the figure AB and CD are the perpendicular diameters of the circle with center at the origin. If B(3,0) then
a) Write the coordinates of C
b) What is the area of the square ABCD
Answer:
a) (0, 3)
b) BC = 3√2 Area = \(\frac{d^2}{2}=\frac{6^2}{2}\) = 18 Sq. units
Question 24.
O is the origin of corrdinates and OABC is a rectangle. If B (3, 4)
a) Write the coordinates A of C
b) If OADE is the reflection of the rectangle on x axis then write the coordinates of D and E
Answer:
a) 4(3,0), C(0, 4)
b) D(3, -4) and E(0, -4)
Question 25.
(2, 3) is a point on a circle with center at the origin
a) What is the radius of this circle
b) Write the coordinates of a point where the circle cut the axes
Answer:
a) Radius = \(\sqrt{2^2+3^2}=\sqrt{13}\)
b) (\(\sqrt{13}\) ,0) (0, \(\sqrt{13}\)) (- \(\sqrt{13}\),0) (0, 7\(\sqrt{13}\) )
Question 26.
A(-4, -1) and B(4, -1) are the vertices of the triangle ABC shown in the figure
a) Write the coordinate of P
b) If the altitude CP = 5 then write the coorinates of C
Answer:
a) (0, – 1)
b) C(0, 4)
Question 27.
A(1, 1), B(4, 1) and C(1, 5) are the vertices of a triangle
a) By observing the vertices write the largest angle of this triangle.
b) What is the length of BC ?
c) What is the radius of the circle passing through the vertices?
Answer:
a) 90°
Since AB is parallel to x axis and AC parallel to y axis, ∠A = 90°
b) BC = \(\sqrt{(1-4)^2+(5-1)^2}=\sqrt{(-3)^2+4^2}=\sqrt{25}\) = 5
c) \(\frac{5}{2}\)
Question 28.
A(2, 0) B(- 6, – 2) C(- 4,- 4) and D(4, – 2) are the vertices of a quadrilateral
a) Find the sides of the quadrilateral
b) Find the length of the diagonals
c) Suggest a suitable name to this quadrilateral
Answer:
a) AB = \(\sqrt{\left(2-^{-} 6\right)^2+\left(0-^{-} 2\right)^2}=\sqrt{8^2+2^2}=\sqrt{68}\)
BC = \(\sqrt{\left(-6-^{-} 4\right)^2+\left(-2-^{-} 4\right)^2}=\sqrt{(-2)^2+2^2}=2 \sqrt{2}\)
CD = \(\sqrt{\left(4-^{-} 4\right)^2+\left(-2-^{-} 4\right)^2}=\sqrt{8^2+2^2}=\sqrt{68}\)
AD = \(\sqrt{(4-2)^2+(-2-0)^2}=\sqrt{2^2+(-2)^2}=2 \sqrt{2}\)
b) AC = \(\sqrt{52}\), BD = 10
c) Opposite sides are equal and diagonals are not equal. So it is a parallelogram.
Question 29.
The y-axis is the tangent to the circle at the origin of coordinates. (5,0) is the center of the circle.
a) Write the coordinates of A
b) If CD is the diameter perpendicular to x axis then write the coordinates of C and D
c) P is a point on this circle such that OP = 8. Find the length AP.
Answer:
a) (10, 0)
b) C(5, 5), D(5, 5)
c) Triangle OPA is a right triangle. AP= 6
Question 30.
As you know if a and b are the parallel sides and h is the distance between the parallel sides then the area of the trapezium is \(\frac{1}{2}\) h (a+b)
In the figure you can see three trapeziums and a triangle with vertices A(1, 3), B(8, 5), and C(4, 10)
a) Write the length of PA, QC and RB which are the parallel sides of the trapeziums
b) Calculate the area of APQC, CQRB.
c) Calculate the area of PABR
d) Find the area of triangle ABC
Answer:
a) PA = 3, QC = 10, RB = 5
b) PQ = 4 – 1 = 3
Area = \(\frac{1}{2}\) × 3 × (3 + 10)
= \(\frac{39}{2}\)
= 19.5 sq. units
QR = 8 – 4 = 4
Area = \(\frac{1}{2}\) × 4 × (10 + 5)
= \(\frac{60}{2}\)
= 30 sq. units
c) PR = 8 – 1 = 7
Area = \(\frac{1}{2}\) × 7 × (3 + 5)
= \(\frac{56}{2}\)
= 28 sq. units
d) Area = 19.5 + 30 – 28 = 21.5 sq. units