Question

The point on y-axis which is at a distance 5 unit from the point (-5, 7) is ___________

(a) (7, 0)

(b) (0, 7)

(c) (1, 7)

(d) (7, 7)

I had been asked this question during an online exam.

My enquiry is from Geometry topic in chapter Coordinate Geometry of Mathematics – Class 10

Answer 1

Right choice is (b) (0, 7)

Easiest explanation: Let the point on y-axis be (0, y)

Distance between (-5, 7) and (0, y) = \( \sqrt {(x_2-x_1)^2 + (y_2-y_1)^2} \)

= \( \sqrt {(0 + 5)^2 + (y-7)^2} \)

= \( \sqrt {y^2-14y + 49 + 25} \)

= \( \sqrt {y^2-14y + 74} \)

The distance between (-5, 7) and (0, y) is 5

∴ \( \sqrt {y^2-14y + 74} \) = 5

Squaring on both sides, we get,

y^2 – 14y + 74 = 25

y^2 – 14y + 49 = 0

y = 7, 7

Hence, the point is (0, 7)