Question

1. triangle abc is shown on the coordinate plane. the triangle is dilated by using the rule (x,y)→(³ x,³ y) to graph triangle def. list and graph the new coordinates.

Explanation:

Since the original coordinates of points A, B, and C are not given in the problem description, we'll assume the general - case steps for dilation. Let the coordinates of point A be \((x_A,y_A)\), point B be \((x_B,y_B)\), and point C be \((x_C,y_C)\).

Step1: Apply dilation rule to point A

The dilation rule is \((x,y)\to(3x,3y)\). For point A with coordinates \((x_A,y_A)\), the new coordinates \(A'\) will be \((3x_A,3y_A)\).

Step2: Apply dilation rule to point B

For point B with coordinates \((x_B,y_B)\), using the rule \((x,y)\to(3x,3y)\), the new coordinates \(B'\) will be \((3x_B,3y_B)\).

Step3: Apply dilation rule to point C

For point C with coordinates \((x_C,y_C)\), using the rule \((x,y)\to(3x,3y)\), the new coordinates \(C'\) will be \((3x_C,3y_C)\).

To graph the new triangle \(DEF\) (formed by \(A'\), \(B'\), and \(C'\)):

1. Locate the new \(x\) - and \(y\) - coordinates of \(A'\), \(B'\), and \(C'\) on the coordinate plane.
2. Connect the points \(A'\), \(B'\), and \(C'\) to form triangle \(DEF\).

If we assume \(A=(2,2)\), \(B=(4,2)\), \(C=(3,4)\):

• \(A'=(3\times2,3\times2)=(6,6)\)
• \(B'=(3\times4,3\times2)=(12,6)\)
• \(C'=(3\times3,3\times4)=(9,12)\)

Answer:

If \(A=(x_A,y_A)\), \(A'=(3x_A,3y_A)\); if \(B=(x_B,y_B)\), \(B'=(3x_B,3y_B)\); if \(C=(x_C,y_C)\), \(C'=(3x_C,3y_C)\)

(In a real - case scenario, you need to substitute the actual coordinates of A, B, and C from the graph to get the exact new coordinates)