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 - statement, we'll assume the general form of applying the dilation rule. Let the coordinates of point \(A=(x_1,y_1)\), point \(B=(x_2,y_2)\) and point \(C=(x_3,y_3)\).

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

Step3: Apply dilation rule to point C

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

To graph the new coordinates, if you know the original coordinates of \(A\), \(B\), and \(C\):

1. First, find the \(x\) - coordinate of the new point by multiplying the original \(x\) - coordinate by 3.
2. Then, find the \(y\) - coordinate of the new point by multiplying the original \(y\) - coordinate by 3.
3. Plot the new points \(A'\), \(B'\), and \(C'\) on the given coordinate plane.

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

Step4: Calculate \(A'\)

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

Step5: Calculate \(B'\)

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

Step6: Calculate \(C'\)

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

Answer:

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