Questions: The vertices of triangle DEP are D(-3,-3), E(-2,-4), and F(-2,0). Graph triangle DEF and its image after reflection in the line y=-x.

Transcript text: The vertices of $\triangle D E P$ are $D(-3,-3), E(-2,-4)$ and $F(-2,0)$. Graph $\triangle D E F$ and its image after reflection in the line $y=-x$.

Solution

Solution Steps

Step 1: Identify the vertices of the triangle

The vertices of triangle $ \Delta DEF $ are given as:

$ D(-3, -3) $
$ E(-2, -4) $
$ F(-2, 0) $

Step 2: Reflect each vertex over the line $ y = -x $

To reflect a point $(x, y)$ over the line $ y = -x $, swap the coordinates and change their signs:

$ D(-3, -3) $ becomes $ D'(-(-3), -(-3)) = D'(3, 3) $
$ E(-2, -4) $ becomes $ E'(-(-4), -(-2)) = E'(4, 2) $
$ F(-2, 0) $ becomes $ F'(0, 2) $

Step 3: Plot the original and reflected vertices

Original vertices: $ D(-3, -3) $, $ E(-2, -4) $, $ F(-2, 0) $
Reflected vertices: $ D'(3, 3) $, $ E'(4, 2) $, $ F'(0, 2) $

Final Answer

The reflected triangle $ \Delta D'E'F' $ has vertices at:

$ D'(3, 3) $
$ E'(4, 2) $
$ F'(0, 2) $

Plot these points on the graph to visualize the reflection.

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