Question

fill in the blank 8 points 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\)

Explanation:

To dilate a point \((x, y)\) with a scale factor \(k\) centered at the origin, we use the rule \((x, y) \to (kx, ky)\). We will apply this rule to each vertex of the quadrilateral.

Step 1: Dilate point \(A(-4, 1)\)

Using the dilation rule with \(k = 3\), we multiply the \(x\)-coordinate and \(y\)-coordinate by 3.
For \(A(-4, 1)\):
\(x\)-coordinate: \(-4\times3=-12\)
\(y\)-coordinate: \(1\times3 = 3\)
So, the new coordinates for \(A\) are \((-12, 3)\).

Step 2: Dilate point \(B(-2, 3)\)

Using the dilation rule with \(k = 3\):
\(x\)-coordinate: \(-2\times3=-6\)
\(y\)-coordinate: \(3\times3 = 9\)
So, the new coordinates for \(B\) are \((-6, 9)\).

Step 3: Dilate point \(C(0, -2)\)

Using the dilation rule with \(k = 3\):
\(x\)-coordinate: \(0\times3 = 0\)
\(y\)-coordinate: \(-2\times3=-6\)
So, the new coordinates for \(C\) are \((0, -6)\).

Step 4: Dilate point \(D(-5, -2)\)

Using the dilation rule with \(k = 3\):
\(x\)-coordinate: \(-5\times3=-15\)
\(y\)-coordinate: \(-2\times3=-6\)
So, the new coordinates for \(D\) are \((-15, -6)\).

Answer:

The new coordinates of the vertices after dilation are \(A(-12, 3)\), \(B(-6, 9)\), \(C(0, -6)\), and \(D(-15, -6)\).