Question

give the new coordinates for dilating quadrilateral abcd with vertices a(-4, 1), b(-2, 3), c(0, -2), and d(-5, -2): k = 3
grid image
write the numerical answer (ie if you get 2 for your answer, type 2 not two)
a( type your answer... , type your answer... )
b( type your answer... , type your answer... )
c( type your answer... , type your answer... )
d( type your answer... , type your answer... )

Explanation:

Step1: Recall dilation rule

To dilate a point \((x, y)\) with a scale factor \(k\), the new coordinates \((x', y')\) are given by \(x' = k \times x\) and \(y' = k \times y\).

Step2: Dilate point A(-4, 1)

For point \(A(-4, 1)\) and \(k = 3\):
\(x' = 3\times(-4)= -12\)
\(y' = 3\times1 = 3\)
So, \(A'(-12, 3)\)

Step3: Dilate point B(-2, 3)

For point \(B(-2, 3)\) and \(k = 3\):
\(x' = 3\times(-2)= -6\)
\(y' = 3\times3 = 9\)
So, \(B'(-6, 9)\)

Step4: Dilate point C(0, -2)

For point \(C(0, -2)\) and \(k = 3\):
\(x' = 3\times0 = 0\)
\(y' = 3\times(-2)= -6\)
So, \(C'(0, -6)\)

Step5: Dilate point D(-5, -2)

For point \(D(-5, -2)\) and \(k = 3\):
\(x' = 3\times(-5)= -15\)
\(y' = 3\times(-2)= -6\)
So, \(D'(-15, -6)\)

Answer:

\(A'(-12, 3)\)
\(B'(-6, 9)\)
\(C'(0, -6)\)
\(D'(-15, -6)\)