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QuestionFind the missing endpoint CC if BB is the midpoint of AC‾\overline{A C} with A(−4,2)A(-4,2) and B(6,−1)B(6,-1).

Studdy Solution

STEP 1

Assumptions1. Point B is the midpoint of line segment AC. . The coordinates of point A are (-4,).
3. The coordinates of point B are (6,-1).
4. We need to find the coordinates of point C.

STEP 2

The formula for the midpoint of a line segment with endpoints (x1,y1)(x1, y1) and (x2,y2)(x2, y2) is given byMidpoint=(x1+x22,y1+y22)Midpoint = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)

STEP 3

Given that B is the midpoint, we can set up the following equations to find the coordinates of C6=−+xC26 = \frac{- + x_C}{2}−1=2+yC2-1 = \frac{2 + y_C}{2}

STEP 4

olving the first equation for xCx_C, we get6=−4+xC26 = \frac{-4 + x_C}{2}12=−4+xC12 = -4 + x_CxC=12+4x_C =12 +4

STEP 5

Calculate the value of xCx_CxC=12+4=16x_C =12 +4 =16

STEP 6

olving the second equation for yCy_C, we get−1=2+yC2-1 = \frac{2 + y_C}{2}−2=2+yC-2 =2 + y_CyC=−2−2y_C = -2 -2

STEP 7

Calculate the value of yCy_CyC=−2−2=−4y_C = -2 -2 = -4

STEP 8

The coordinates of the missing endpoint C are therefore (16,−4)(16, -4).
The coordinates of point C are (16,−4)(16, -4).

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