Question

The midpoint of AB is M (2, -1). If the coordinates of A are (1, 6), what are the

Answer 1

The coordinates of B are (3, -8). Where the line-segment AB has the midpoint at M with coordinates (2, -1).

How to calculate the midpoint?

The midpoint on a line segment with two endpoints (x1, y1) and (x2, y2) is

Midpoint (x, y) = ($\frac{x1+x2}{2}$, $\frac{y1+y2}{2}$)

Calculation:

The given line segment is AB with coordinates A(1, 6) and B(x2, y2).

M is the midpoint of line segment AB. Its coordinates are M(2, -1)

Then, the coordinates of B are calculated by

M(x, y) = ($\frac{x1+x2}{2}$, $\frac{y1+y2}{2}$)

(2, -1) = ($\frac{1+x2}{2}$, $\frac{6+y2}{2}$)

In comparing both sides,

2 = (1 + x2)/2 and -1 = (6 + y2)/2

On simplifying,

2 = (1 + x2)/2

⇒ 4 = (1 + x2)

⇒ 1 + x2 = 4

⇒ x2 = 4 - 1

∴ x2 = 3

-1 = (6 + y2)/2

⇒ 6 + y2 = -2

⇒ y2 = -2 - 6

∴ y2 = -8

Thus, the coordinates of the required point are B(3, -8).

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