Question

lesson 5 practice problems a. here are some points: grid image what are the coordinates of a, b, and c after a translation to the right by 4 units and up 1 unit?

Explanation:

Step1: Find original coordinates

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

• Point \( A \): Looking at the grid, the \( x \)-coordinate (horizontal) is \( 5 \), and the \( y \)-coordinate (vertical) is \( 6 \), so \( A = (5, 6) \).
• Point \( B \): The \( x \)-coordinate is \( 2 \), and the \( y \)-coordinate is \( -3 \), so \( B = (2, -3) \).
• Point \( C \): The \( x \)-coordinate is \( -1 \), and the \( y \)-coordinate is \( 0 \), so \( C = (-1, 0) \).

Step2: Apply translation rules

A translation to the right by \( 4 \) units means we add \( 4 \) to the \( x \)-coordinate, and a translation up by \( 1 \) unit means we add \( 1 \) to the \( y \)-coordinate. The translation rule is \( (x, y) \to (x + 4, y + 1) \).

For point \( A \):

Substitute \( x = 5 \) and \( y = 6 \) into the translation rule:
\( x + 4 = 5 + 4 = 9 \)
\( y + 1 = 6 + 1 = 7 \)
So, the new coordinates of \( A \) are \( (9, 7) \).

For point \( B \):

Substitute \( x = 2 \) and \( y = -3 \) into the translation rule:
\( x + 4 = 2 + 4 = 6 \)
\( y + 1 = -3 + 1 = -2 \)
So, the new coordinates of \( B \) are \( (6, -2) \).

For point \( C \):

Substitute \( x = -1 \) and \( y = 0 \) into the translation rule:
\( x + 4 = -1 + 4 = 3 \)
\( y + 1 = 0 + 1 = 1 \)
So, the new coordinates of \( C \) are \( (3, 1) \).

Answer:

• Coordinates of \( A \) after translation: \( (9, 7) \)
• Coordinates of \( B \) after translation: \( (6, -2) \)
• Coordinates of \( C \) after translation: \( (3, 1) \)