Question

What will be the coordinates of the midpoint of the line segment joining the points (-5, 10) and(15, 2)?

(a) (-5, -6)

(b) (-5, 6)

(c) (5, 6)

(d) (5, -6)

I had been asked this question in an international level competition.

Enquiry is from Geometry in chapter Coordinate Geometry of Mathematics – Class 10

Answer 1

Correct answer is (c) (5, 6)

To explain I would say: Midpoint lies in the center of the line segment

Hence, it divides the line in the ratio 1:1

Using, section formula x = \(\frac {mx_2+nx_1}{m+n}\) and y = \(\frac {my_2+ny_1}{m+n}\)

The points are A(-5, 10) and B(15, 2) and the ratio is 1:1

∴ x = \(\frac {1(-5)+1(15)}{2} = \frac {-5+15}{2} = \frac {10}{2}\) = 5

y = \(\frac {1(2)+1(10)}{2} = \frac {2+10}{2} = \frac {12}{2}\) = 6

Hence, the point is (5,6).