Question

The line ab has midpoint (-2, 4) a has coordinates (3, -2) find the coordinates of b

Answer 1

Answer:

b = (- 7, 10 )

Step-by-step explanation:

Given the endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ $\frac{1}{2}$ (x₁ + x₂ ), $\frac{1}{2}$ (y₁ + y₂ ) ]

let the coordinates of b = (x, y ) then use the formula and equate to the coordinates of the midpoint, that is

$\frac{1}{2}$ (x + 3) = - 2 ( multiply both sides by 2 )

x + 3 = - 4 ( subtract 3 from both sides )

x = - 7

$\frac{1}{2}$ (y - 2) = 4 ( multiply both sides by 2 )

y - 2 = 8 ( add 2 to both sides )

y = 10

Thus the coordinates of b are (- 7, 10 )