Question

graph the image of δbcd after a translation 5 units right.

Explanation:

Step1: Identify coordinates of B, C, D

First, find the coordinates of the vertices of \( \triangle BCD \). From the graph:

• \( B \): Let's assume the grid. Looking at the x - coordinate (horizontal) and y - coordinate (vertical). The x - coordinate of B is - 5 (since it's 5 units left of the origin on the x - axis) and y - coordinate is - 6. So \( B(-5,-6) \).
• \( C \): x - coordinate is - 5, y - coordinate is 3. So \( C(-5,3) \).
• \( D \): x - coordinate is - 4, y - coordinate is - 5. So \( D(-4,-5) \).

Step2: Apply translation rule (5 units right)

A translation 5 units right means we add 5 to the x - coordinate of each vertex (since moving right on the x - axis increases the x - value, and the y - value remains the same). The translation rule for a point \( (x,y) \) is \( (x + 5,y) \).

• For \( B(-5,-6) \):

New x - coordinate: \( - 5+5 = 0 \), y - coordinate remains - 6. So \( B'(0,-6) \).

• For \( C(-5,3) \):

New x - coordinate: \( - 5 + 5=0 \), y - coordinate remains 3. So \( C'(0,3) \).

• For \( D(-4,-5) \):

New x - coordinate: \( - 4+5 = 1 \), y - coordinate remains - 5. So \( D'(1,-5) \).

Step3: Graph the new triangle

Plot the points \( B'(0,-6) \), \( C'(0,3) \), and \( D'(1,-5) \) on the coordinate plane and connect them to form the image of \( \triangle BCD \) after the translation.

Answer:

The image of \( \triangle BCD \) after a translation 5 units right has vertices \( B'(0,-6) \), \( C'(0,3) \), and \( D'(1,-5) \). (To graph, plot these points and connect them.)