12. $$ B $$ is the midpoint of $$ \overline{A C} $$ and $$ E $$ is the midpoint of $$ \overline{B D} $$. If $$ A(-9,-4), C(-1,6) $$, and $$ E(-4,-3) $$, find the coordinates of $$ D $$. $$ \left(\frac{-9+1}{2}, \frac{-4-6}{2}\right) \quad(-4,-5) $$ $$ (-9,-4)(-4,-5) $$ $$ (-4,-3), E $$ $$ (-1,6) $$ 4

Question

UpStudy AI · Accepted Answer

$$
\textbf{Step 1: Find the midpoint } B \textbf{ of } \overline{AC}.
$$
Given $$ A(-9, -4) $$ and $$ C(-1, 6) $$, the coordinates of $$ B $$ are found using the midpoint formula:
$$
B = \left(\frac{-9 + (-1)}{2}, \frac{-4 + 6}{2}\right) = \left(\frac{-10}{2}, \frac{2}{2}\right) = (-5, 1).
$$

$$
\textbf{Step 2: Use the midpoint } E \textbf{ to find } D.
$$
$$ E $$ is the midpoint of $$ \overline{BD} $$ and is given as $$ E(-4, -3) $$. Let $$ D = (x, y) $$.

The midpoint of $$ B(-5,1) $$ and $$ D(x,y) $$ is:
$$
E = \left(\frac{-5 + x}{2}, \frac{1 + y}{2}\right) = (-4, -3).
$$

Now, equate the coordinates:

For the $$ x $$-coordinate:
$$
\frac{-5 + x}{2} = -4 \quad \Rightarrow \quad -5 + x = -8 \quad \Rightarrow \quad x = -3.
$$

For the $$ y $$-coordinate:
$$
\frac{1 + y}{2} = -3 \quad \Rightarrow \quad 1 + y = -6 \quad \Rightarrow \quad y = -7.
$$

$$
\textbf{Final Answer: } D = (-3, -7).
$$
The coordinates of $$ D $$ are $$ (-3, -7) $$.

is the midpoint of and is the midpoint of . If , and , find
the coordinates of .

4

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Geometry Questions

is the midpoint of and is the midpoint of . If , and , find the coordinates of . 4