Triangle DEF has vertices at D(−3, 5), E(−10, 4), and F(−11, 8). Triangle D′E′F′ is the image of triangle DEF after a reflection. Determine the line of reflection if E′ is located at (10, 4).

Question

y = −4
x = 10
y-axis
x-axis

Answer 1

To determine the line of reflection for triangle DEF to triangle D'E'F', we first note that point E(−10, 4) reflects to E'(10, 4).

This means the line of reflection must be equidistant from points E and E'. Since both points share the same y-coordinate, the line of reflection must be a vertical line that bisects the x-coordinates of E and E'.

The x-coordinate of E is -10, and the x-coordinate of E' is 10. The midpoint between these two x-coordinates is:

\[ \text{Midpoint} = \frac{-10 + 10}{2} = 0 \]

Thus, the line of reflection is the vertical line \( x = 0 \), also known as the y-axis.

So, the correct answer is: y-axis.