Question

in the coordinate plane shown, point b was transformed using the coordinate rule ((x, y) \to (3x, 3y)).

1. add these auxiliary points and lines to create 2 right triangles: label the origin ( p ). plot points ( m = (2, 0) ) and ( n = (6, 0) ). draw segments ( pb ), ( mb ), and ( nb ).

draw on the image.

Explanation:

1. First, identify the origin (0,0) on the grid and label it as point P.
2. Locate the coordinates of point B: from the grid, B is at (2, 3). Plot point M at (2, 0) on the x-axis directly below B.
3. Locate the coordinates of point B': from the grid, B' is at (6, 9). Plot point N at (6, 0) on the x-axis directly below B'.
4. Draw a straight line connecting P(0,0) to B'(6,9), a straight line connecting M(2,0) to B(2,3), and a straight line connecting N(6,0) to B'(6,9). This forms the two required right triangles: triangle PMB and triangle PNB'.

Answer:

The completed coordinate plane will have:

• Origin (0,0) labeled as P
• Point M=(2,0) plotted on the x-axis
• Point N=(6,0) plotted on the x-axis
• Segment $PB'$ connecting (0,0) to (6,9)
• Segment $MB$ connecting (2,0) to (2,3)
• Segment $NB'$ connecting (6,0) to (6,9)