Segment $A B$ is reflected in the $y$-axis to obtain $E D$. Segment $B C$ is reflected in the $y$-axis to obtain $D C$. Determine the sum of the slopes of $D C$ and $E D$.

![](https://cdn.mathpix.com/cropped/2024_04_17_d49dd011068fc0fd28d1g-1.jpg?height=420&width=542&top_left_y=1237&top_left_x=1342)
Solution 1

The slope of segment $A B$ is $\frac{0-6}{-2-(-4)}=-3$.

Since $E D$ is the reflection of $A B$ in the $y$-axis, its slope is the negative of the slope of $A B$. This means the slope of $E D$ is 3 .

Similarly, the slope of segment $B C$ is $\frac{4-0}{0-(-2)}=2$, so the slope of $D C$ is -2 .

Therefore, the sum of the slopes is $-2+3=1$.

## Solution 2

From the information given, $E$ is the reflection in the $y$-axis of $A$ and $D$ is the reflection in the $y$-axis of $B$.

Since the coordinates of $A$ are $(-4,6)$, this means the coordinates of $E$ are $(4,6)$. Similarly, since the coordinates of $B$ are $(-2,0)$, the coordinates of $D$ are $(2,0)$.

![](https://cdn.mathpix.com/cropped/2024_04_17_a164435ebfb99ea5f1c4g-02.jpg?height=466&width=591&top_left_y=2147&top_left_x=824)

The slope of segment $D C$ is $\frac{0-4}{2-0}=-2$. The slope of $E D$ is $\frac{6-0}{4-2}=3$, so the sum of the slopes is $-2+3=1$.

ANSWER: 1

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