Question

Endpoint: (-4, 8), midpoint: (3,-4)

Find the other endpoint

Explain please

Answer 1

Answer: (10,-16)

Explanation:

`A(-4,8)\ \ \ \ C(3,-4)\ \ \ \ \ B(x_B,y_B)=?\\`

See the graph below.

`\displaystyle\\\boxed {x_C=(x_A+x_B)/(2) }\\\\`

Multiply both parts of the equation by 2:

`2x_C=x_A+x_B\\2x_C-x_A=x_A+x_B-x_A\\2x_C-x_A=x_B`

Hence,

`x_B=2*3-(-4)\\x_B=6+4\\x_B=10`

`\displaystyle\\\boxed {y_C=(y_A+y_B)/(2) }`

Multiply both parts of the equation by 2:

`2y_C=y_A+y_B\\2y_C-y_A=y_A+y_B-y_A\\2y_C-y_A=y_B`

Hence,

`y_B=2*(-4)-8\\y_B=-8-8\\y_B=-16\\Thus,\ B(10,-16)`