Question

the vertices of △abc are a(-5,5), b(-2,5), and c(-4,3). if △abc is reflected across the line y = -1 to produce the image △abc, find the coordinates of the vertex c. the coordinates of c after a reflection across the line y = -1 are (type an ordered pair.)

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected across the line $y = k$, the new - y - coordinate is $y'=2k - y$ and the x - coordinate remains the same. Here $k=-1$.

Step2: Identify the original coordinates of C

The original coordinates of point C are $(-4,3)$.

Step3: Calculate the new y - coordinate

Using the formula $y'=2k - y$, substitute $k = - 1$ and $y = 3$. Then $y'=2\times(-1)-3=-2 - 3=-5$.

Step4: Determine the new coordinates of C'

The x - coordinate of C' is the same as the x - coordinate of C, which is $x=-4$. So the coordinates of C' are $(-4,-5)$.

Answer:

$(-4,-5)$