Question

nc.8.g.3 4. draw a dilation of triangle abc with center (0,0) and a scale factor of 2. label the new triangle abc. (1 point)

Explanation:

Step1: Identify coordinates of A, B, C

First, we need to find the coordinates of the original triangle's vertices. From the graph (assuming the grid is standard with each square as 1 unit):

• Let's assume point \( A \) has coordinates \( (-2, -4) \) (since it's 2 units left on the x - axis and 4 units down on the y - axis from the origin \((0,0)\)).
• Point \( B \) has coordinates \( (-2, 2) \) (2 units left on the x - axis and 2 units up on the y - axis).
• Point \( C \) has coordinates \( (2, 2) \) (2 units right on the x - axis and 2 units up on the y - axis).

Step2: Apply dilation with scale factor 2 and center (0,0)

The rule for dilation with center \((0,0)\) and scale factor \( k \) is \((x,y)\to(kx,ky)\).

• For point \( A(-2,-4) \):

Applying the dilation rule, \( A'=(2\times(-2),2\times(-4))=(-4,-8) \)

• For point \( B(-2,2) \):

Applying the dilation rule, \( B'=(2\times(-2),2\times2)=(-4,4) \)

• For point \( C(2,2) \):

Applying the dilation rule, \( C'=(2\times2,2\times2)=(4,4) \)

Step3: Plot the new points

Plot the points \( A'(-4,-8) \), \( B'(-4,4) \), and \( C'(4,4) \) on the coordinate plane and connect them to form triangle \( A'B'C' \).

Answer:

To draw the dilated triangle \( A'B'C' \):

1. Find the original coordinates of \( A(-2,-4) \), \( B(-2,2) \), \( C(2,2) \).
2. Apply dilation: \( A'(-4,-8) \), \( B'(-4,4) \), \( C'(4,4) \).
3. Plot these points and connect them. The new triangle \( A'B'C' \) will have sides twice as long as triangle \( ABC \) and be centered at the origin with the same shape (similar triangle).