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, we'll assume the original coordinates of \(A=(x_1,y_1)\), \(B=(x_2,y_2)\), \(C=(x_3,y_3)\) for the general - case solution.

Step1: Apply dilation rule to point A

The dilation rule is \((x,y)\to(3x,3y)\). For point \(A=(x_1,y_1)\), the new coordinates \(A'=(3x_1,3y_1)\).

Step2: Apply dilation rule to point B

For point \(B=(x_2,y_2)\), using the rule \((x,y)\to(3x,3y)\), the new coordinates \(B'=(3x_2,3y_2)\).

Step3: Apply dilation rule to point C

For point \(C=(x_3,y_3)\), using the rule \((x,y)\to(3x,3y)\), the new coordinates \(C'=(3x_3,3y_3)\).

To graph the new points:

1. Locate the original points \(A\), \(B\), and \(C\) on the coordinate - plane.
2. Multiply the \(x\) - coordinate and \(y\) - coordinate of each point by 3 to get the new points \(A'\), \(B'\), and \(C'\).
3. Plot the new points \(A'\), \(B'\), and \(C'\) on the same coordinate - plane and connect them to form triangle \(DEF\).

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

Step1: Calculate \(A'\)

\(x\) - coordinate of \(A'\): \(3\times2 = 6\)
\(y\) - coordinate of \(A'\): \(3\times2=6\), so \(A'=(6,6)\)

Step2: Calculate \(B'\)

\(x\) - coordinate of \(B'\): \(3\times4 = 12\)
\(y\) - coordinate of \(B'\): \(3\times4 = 12\), so \(B'=(12,12)\)

Step3: Calculate \(C'\)

\(x\) - coordinate of \(C'\): \(3\times4=12\)
\(y\) - coordinate of \(C'\): \(3\times2 = 6\), so \(C'=(12,6)\)

Answer:

If \(A=(2,2)\), \(B=(4,4)\), \(C=(4,2)\), then \(A'=(6,6)\), \(B'=(12,12)\), \(C'=(12,6)\)