Question

write the coordinates of the vertices after a translation 4 units up.
b((
c(
d(

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points \( B \), \( C \), and \( D \) from the graph.

• For point \( B \): Looking at the grid, the \( x \)-coordinate is \(-4\) and the \( y \)-coordinate is \( 2 \), so \( B(-4, 2) \).
• For point \( C \): The \( x \)-coordinate is \( 6 \) and the \( y \)-coordinate is \( 2 \), so \( C(6, 2) \).
• For point \( D \): The \( x \)-coordinate is \(-4\) and the \( y \)-coordinate is \(-8\), so \( D(-4, -8) \).

Step2: Apply translation (4 units up)

A translation of 4 units up means we add 4 to the \( y \)-coordinate of each point (the \( x \)-coordinate remains the same). The translation rule for a vertical shift up by \( k \) units is \( (x, y) \to (x, y + k) \), here \( k = 4 \).

• For \( B' \): Take \( B(-4, 2) \), add 4 to the \( y \)-coordinate: \( y = 2 + 4 = 6 \), so \( B'(-4, 6) \).
• For \( C' \): Take \( C(6, 2) \), add 4 to the \( y \)-coordinate: \( y = 2 + 4 = 6 \), so \( C'(6, 6) \).
• For \( D' \): Take \( D(-4, -8) \), add 4 to the \( y \)-coordinate: \( y = -8 + 4 = -4 \), so \( D'(-4, -4) \).

Answer:

\( B'(-4, 6) \)
\( C'(6, 6) \)
\( D'(-4, -4) \)