QuestionFind the missing endpoint $C$ if $B$ is the midpoint of $\overline{A C}$ , given $A(1,7)$ and $B(-3,1)$ .

Studdy Solution

STEP 1

Assumptions1. Point B is the midpoint of line segment AC. . The coordinates of point A are (1,7).
3. The coordinates of point B are (-3,1).
4. We need to find the coordinates of point C.

STEP 2

The formula for finding the midpoint of a line segment is $B = \left(\frac{x_A + x_C}{2}, \frac{y_A + y_C}{2}\right)$

STEP 3

We know the coordinates of point B and point A, so we can set up the following system of equations to solve for the coordinates of point C.
$-3 = \frac{1 + x_C}{2}$ $1 = \frac{7 + y_C}{2}$

STEP 4

To solve for $x_C$ , we multiply both sides of the first equation by2 and then subtract1.
$-3 \times2 =1 + x_C$ $-6 -1 = x_C$

STEP 5

Calculate the value of $x_C$ .
$x_C = - -1 = -7$

STEP 6

To solve for $y_C$ , we multiply both sides of the second equation by2 and then subtract.
$1 \times2 = + y_C$ $2 - = y_C$

STEP 7

Calculate the value of $y_C$ .
$y_C =2 -7 = -5$

STEP 8

Now that we have the values for $x_C$ and $y_C$ , we can write the coordinates of point C.
$C = (x_C, y_C)$

STEP 9

Plug in the values for $x_C$ and $y_C$ to get the coordinates of point C.
$C = (-7, -5)$ The coordinates of the missing endpoint C are (-7, -5).

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