Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Coordinate Geometry:

Exercise 7.2

Very Short Answer Type Questions (Q. No. 1-6)

Write whether True or False and justify your answer

Question. 1 ΔABC with vertices A (– 2, 0), B (2, 0) and C (0, 2) is similar to ΔDEF with vertices D (-4, 0), E (4, 0) and F (0, 4).

Solution. True

Explanation:

Here, we see that sides of ΔABC and ΔFDE are proportional

Therefore, by SSS similarity rule both the triangles are similar.        

Question. 2 The point P (-4, 2) lies on the line segment joining the points A (-4, 6) and B (-4, -6).

Solution. True

Explanation:

If we plot all the points P (-4, 2), A (-4, 6) and B (-4, -6) on the graph paper then, we will find, point P (-4, 2) lies on the line segment joining the points A (-4, 6) and B (-4, -6),

Question. 3 The points (0, 5), (0, -9) and (3, 6) are collinear.

Solution. False

Given, x₁ = 0, x₂ = 0 , x₃ = 3 and  y₁ = 5, y₂ = −9, y₃ = 6

Three points will be collinear if the area of triangle formed by these three points is zero.

Now, area of triangle formed by three points (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given as,            

As the area of triangle formed by the points (0, 5), (0, ‒ 9) and (3, 6) is non-zero, hence the points are non-collinear.

Question. 4 Point P (0, 2) is the point of intersection of Y-axis and perpendicular bisector of line segment joining the points A (‒1, 1) and B (3, 3).

Solution. False

For P(0, 2) to be the point of intersection of y–axis and perpendicular bisector of the line joining the points A(–1, 1) and B(3, 3), P must be equidistant from A and B.

i.e., PA = PB

Question. 5 The points A (3, 1), B (12, -2) and C (0, 2) cannot be vertices of a triangle.

Solution. True

For any three points to be the vertices of a triangle, the area of that triangke must be non-zero.

Now, area of triangle formed by three points (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given as,            

Since, area of ΔABC = 0, therefore, the points, A (3, 1), B (12, ‒2) and C (0, 2) are collinear and can’t be the vertices of a triangle.

Question. 6 The points A (4, 3), B (6, 4), C (5, - 6) and D (-3, 5) are vertices of a parallelogram.

Solution. False

Given points will be the vertices of a parallelogram, if the opposite sides of that parallelogram come out to be equal.

By using distance formula, distance between A (4, 3) and B (6, 4), 

In parallelogram, opposite sides are equal. But, in this case all sides AB, BC, CD and DA are different.

Therefore, given coordinates are not the vertices of a parallelogram.