Question

write the coordinates of the vertices after a translation 2 units left.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex:

• \( T \): From the graph, \( T \) is at \( (0, 0) \).
• \( U \): \( U \) is at \( (0, 9) \) (since it's on the y - axis, x = 0, y = 9).
• \( V \): \( V \) is at \( (4, 10) \) (x = 4, y = 10).
• \( W \): \( W \) is at \( (4, 1) \) (x = 4, y = 1).

Step2: Apply translation rule

The rule for translating a point \( (x,y) \) \( h \) units left is \( (x - h,y) \), where \( h = 2 \) (since we are moving 2 units left).

For point \( T(0,0) \):

Substitute \( x = 0 \), \( y = 0 \), \( h = 2 \) into the translation formula.
New \( x \) - coordinate: \( 0-2=- 2 \)
New \( y \) - coordinate: \( 0 \)
So, \( T'=(-2,0) \)

For point \( U(0,9) \):

Substitute \( x = 0 \), \( y = 9 \), \( h = 2 \) into the translation formula.
New \( x \) - coordinate: \( 0 - 2=-2 \)
New \( y \) - coordinate: \( 9 \)
So, \( U'=(-2,9) \)

For point \( V(4,10) \):

Substitute \( x = 4 \), \( y = 10 \), \( h = 2 \) into the translation formula.
New \( x \) - coordinate: \( 4-2 = 2 \)
New \( y \) - coordinate: \( 10 \)
So, \( V'=(2,10) \)

For point \( W(4,1) \):

Substitute \( x = 4 \), \( y = 1 \), \( h = 2 \) into the translation formula.
New \( x \) - coordinate: \( 4-2=2 \)
New \( y \) - coordinate: \( 1 \)
So, \( W'=(2,1) \)

Answer:

The coordinates of the vertices after translation are \( T'(-2,0) \), \( U'(-2,9) \), \( V'(2,10) \), \( W'(2,1) \)