Question

If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y − 10 = 0, find the value of k.

Answer 1

x + y − 10 = 0

midpoint = `((x_1 + x_2)/2 , (y_1+y_2)/2)`

`(x, y) = ((3+k)/2, 10/2)`

`(x,y) = ((3+k)/2, 5)`

`(3+k)/2 + 5-10 = 0`

`(3+k)/2 = 5`

3 + k = 10

k = 10 − 3 = 7

k = 7