QuestionFind the coordinates of point $B$ if the midpoint $M(0,-2)$ and point $A(8,-8)$ are given.

Studdy Solution

STEP 1

Assumptions1. The midpoint of a line segment is the point that divides the line segment into two equal segments. . The coordinates of the midpoint M are given as $(0, -)$ .
3. The coordinates of point A are given as $(8, -8)$ .
4. We are asked to find the coordinates of point B.

STEP 2

The formula to find the midpoint M of a line segment with endpoints A and B is given by $M = \left(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2}\right)$

STEP 3

We can rearrange the midpoint formula to solve for the x-coordinate of B $x_B =2x_M - x_A$

STEP 4

Substitute the given values into the equation to find $x_B$ $x_B =2(0) -8$

STEP 5

Calculate the x-coordinate of B $x_B =2(0) -8 = -8$

STEP 6

Similarly, we can rearrange the midpoint formula to solve for the y-coordinate of B $y_B =2y_M - y_A$

STEP 7

Substitute the given values into the equation to find $y_B$ $y_B =2(-2) - (-)$

STEP 8

Calculate the y-coordinate of B $y_B =2(-2) - (-8) =4$ So, the coordinates of point B are $(-8,4)$ .

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