Problem

Draw the image of $\triangle A B C$ after a reflection across line $l$. Step 1 Pretend to fold the graph along line $l$ to predict where points $A, B$, and $C$ will land. Step 2 Draw a segment with endpoint A so that the segment is perpendicular to line $l$ and is bisected by line $l$. Label the other endpoint of the segment $A^{\prime}$. Perpendicular lines have opposite-reciprocal slopes. In this case, line l has a slope of $-\frac{1}{1^{\prime}}$ so segment $A A^{\prime}$ must have a slope of $+\frac{1}{1}$. Refer to the top image

Solution

Step 1 :Pretend to fold the graph along line l to predict where points A, B, and C will land.

Step 2 :Draw a segment with endpoint A so that the segment is perpendicular to line l and is bisected by line l. Label the other endpoint of the segment A'.

Step 3 :Perpendicular lines have opposite-reciprocal slopes. In this case, line l has a slope of \(-\frac{1}{1'}\) so segment AA' must have a slope of \(+\frac{1}{1}\).

Step 4 :The problem is asking to reflect a triangle across a line. This involves finding the mirror image of each point of the triangle across the given line. This can be done by drawing a line from each point to the line of reflection that is perpendicular to the line of reflection. The reflected point will be the same distance from the line of reflection but on the opposite side.

Step 5 :The final answer would be the image of the triangle after reflection across line l. This cannot be represented in text or code format.

From Solvely APP
Source: https://solvelyapp.com/problems/18519/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download