Question

if triangle abc is translated 3 units right, what are the coordinates of point a? if triangle abc is translated 2 units down, what are the coordinates of point b? if triangle abc is translated 3 units right and 2 units down, what are the coordinates of point c?

Explanation:

Step1: Identify original coordinates

First, find the original coordinates of the points. From the graph:

• Point \( A \): Let's assume the grid has \( x \) (horizontal) and \( y \) (vertical) axes. Looking at the graph, \( A \) is at \( (0, 5) \), \( B \) at \( (4, 2) \), \( C \) at \( (1, 1) \) (assuming standard grid with \( x \)-axis right and \( y \)-axis up, and each grid square is 1 unit).

Step2: Translate 3 units right (first sub - question: A after 3 right)

For a translation 3 units right, we add 3 to the \( x \)-coordinate. The original \( x \)-coordinate of \( A \) is \( 0 \), so new \( x = 0+3 = 3 \). The \( y \)-coordinate remains the same (\( 5 \)). So new \( A \) is \( (3, 5) \).

Step3: Translate 2 units down (second sub - question: B after 2 down)

For a translation 2 units down, we subtract 2 from the \( y \)-coordinate. Original \( B \) is \( (4, 2) \), so new \( y = 2 - 2=0 \). \( x \)-coordinate remains \( 4 \). So new \( B \) is \( (4, 0) \).

Step4: Translate 3 right and 2 down (third sub - question: C after 3 right and 2 down)

For 3 units right, add 3 to \( x \)-coordinate of \( C \) (original \( x = 1 \), new \( x=1 + 3=4 \)). For 2 units down, subtract 2 from \( y \)-coordinate of \( C \) (original \( y = 1 \), new \( y = 1-2=- 1 \)). So new \( C \) is \( (4, - 1) \).

First sub - question (A after 3 right):

Answer:

\((3, 5)\)

Second sub - question (B after 2 down):