Question

graph each image given the transformation. use correct notation! 1. translation: 4 units left and 1 unit down

Explanation:

Step1: Identify original coordinates

First, we find the coordinates of the vertices of the original figure. Let's assume the grid has each square as 1 unit. From the graph:

• Vertex \( W \): Let's say its coordinates are \( (0, -1) \) (assuming the origin is at the intersection of axes, and counting grid units). Wait, maybe better to look at the positions. Let's re - examine:

Looking at the graph, let's define the coordinates properly. Let's assume the x - axis and y - axis with the origin at the intersection. Let's find the coordinates of \( T \), \( W \), \( V \), \( U \):

• \( T \): Let's say it is at \( (-1, -3) \)
• \( W \): At \( (0, -1) \)
• \( V \): At \( (2, -1) \)
• \( U \): At \( (2, -2) \)

Step2: Apply translation rule

The translation is 4 units left (which means subtract 4 from the x - coordinate) and 1 unit down (subtract 1 from the y - coordinate). The translation rule for a point \( (x,y) \) is \( (x - 4,y - 1) \)

For point \( T(-1,-3) \):

New \( x=-1 - 4=-5 \), New \( y=-3 - 1=-4 \). So \( T'(-5,-4) \)

For point \( W(0,-1) \):

New \( x = 0-4=-4 \), New \( y=-1 - 1=-2 \). So \( W'(-4,-2) \)

For point \( V(2,-1) \):

New \( x = 2-4=-2 \), New \( y=-1 - 1=-2 \). So \( V'(-2,-2) \)

For point \( U(2,-2) \):

New \( x = 2-4=-2 \), New \( y=-2 - 1=-3 \). So \( U'(-2,-3) \)

Step3: Plot the new points

Plot the points \( T'(-5,-4) \), \( W'(-4,-2) \), \( V'(-2,-2) \), \( U'(-2,-3) \) on the coordinate grid and connect them to get the translated figure.

Answer:

The translated figure has vertices at \( T'(-5,-4) \), \( W'(-4,-2) \), \( V'(-2,-2) \), \( U'(-2,-3) \) (and the figure is formed by connecting these points). To graph it, plot these points on the coordinate plane.