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2 years ago

Endpoint: (-4, 8), midpoint: (3,-4) Find the other endpoint Explain please

Mathematics

1 answer:

swat322 years ago

4 0

Answer: (10,-16)

Step-by-step explanation:

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

See the graph below.

$\displaystyle\\\boxed {x_C=\frac{x_A+x_B}{2} }\\\\$

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,

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

$\displaystyle\\\boxed {y_C=\frac{y_A+y_B}{2} }$

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,

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

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E) See attached graph

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