When you are trying to find the endpoint when

Ответ:

lorenzo1beaton

05.02.2022

(x_2,y_2) = (2x_m - x_1 ,2y_m - y_1 )

Step-by-step explanation:

Given

$\left(\frac{x_1+\:x_2}{2},\:\:\frac{y_{1\:}+y_2}{2}\right)\:=\:\left(x_m,\:y_m\right)$

Required

Determine x2, y2

Start by splitting the expression

$x_m = \left(\frac{x_1+\:x_2}{2})$ and $y_m = (\frac{y_{1\:}+y_2}{2})$

Solving for x2 in $x_m = \left(\frac{x_1+\:x_2}{2})$

Multiply through by 2

$2 * x_m = \frac{x_1 + x_2}{2} * 2$

2x_m = x_1 + x_2

Make x2 the subject;

x_2 = 2x_m - x_1

Similarly:

$y_m = (\frac{y_{1\:}+y_2}{2})$

Multiply through by 2

$2 * y_m = \frac{y_1 + y_2}{2} * 2$

2y_m = y_1 + y_2

Make y2 the subject;

y_2 = 2y_m - y_1

Hence:

(x_2,y_2) = (2x_m - x_1 ,2y_m - y_1 )

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