Respuesta :
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) = ([tex]\frac{x1+x2}{2}[/tex], [tex]\frac{y1+y2}{2}[/tex])
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) = ([tex]\frac{x1+x2}{2}[/tex], [tex]\frac{y1+y2}{2}[/tex])
(2, -1) = ([tex]\frac{1+x2}{2}[/tex], [tex]\frac{6+y2}{2}[/tex])
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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