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QuestionFind the missing endpoint DD if E(4,3)E(4,3) is the midpoint of DF‾\overline{D F} with F(5,8)F(5,8). Options: a) D(−1,−5)D(-1,-5) b) D(6,13)D(6,13) c) D(3,−2)D(3,-2) d) D(0.5,5.5)D(0.5,5.5)

Studdy Solution

STEP 1

Assumptions1. Point is the midpoint of line segment $\overline{ F}$ . The coordinates of point are (5,8)(5,8)3. The coordinates of point are $(4,3)$4. We are looking for the coordinates of point

STEP 2

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

STEP 3

We know the coordinates of point and and , so we can set up the following equations to solve for the coordinates of point = \frac{x_D +5}{2}3 = \frac{y_D +8}{2}$$

STEP 4

olving the first equation for xDx_D givesxD=2⋅4−x_D =2 \cdot4 -

STEP 5

Calculate the xx-coordinate of point x_D =2 \cdot4 -5 =3$$

STEP 6

olving the second equation for yDy_D givesyD=2⋅3−8y_D =2 \cdot3 -8

STEP 7

Calculate the yy-coordinate of point y_D =2 \cdot3 - = -2$$

STEP 8

The coordinates of point $$ are $(3, -2)$, so the answer is option c $(3,-2)$.

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