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ΔDEF has coordinates D(3, 1), E(6, 1) and F(6, −3). The triangle is reflected over the x-axis. What is the length of D'F'?

Question

ΔDEF has coordinates D(3, 1), E(6, 1) and F(6, −3).

The triangle is reflected over the x-axis. What is the length of D'F'?

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Solution

To find the length of D'F', we first need to find the coordinates of D' and F' after the reflection over the x-axis.

The reflection of a point (x, y) over the x-axis is (x, -y).

So, the coordinates of D' and F' are:

D'(3, -1) and F'(6, 3)

Now, we can use the distance formula to find the length of D'F':

D'F' = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

D'F' = sqrt[(6 - 3)^2 + (3 - (-1))^2]

D'F' = sqrt[(3)^2 + (4)^2]

D'F' = sqrt[9 + 16]

D'F' = sqrt[25]

D'F' = 5 units.

This problem has been solved

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