Question

problem solving the vertices of a trapezoid are ( a(-2,3) ), ( b(2,3) ), ( c(5,-2) ), and ( d(-2,-2) ). dilate the trapezoid with respect to vertex ( a ) using a scale factor of 2. what are the coordinates of the image? the coordinates of the image are ( a(square,square) ), ( b(square,square) ), ( c(square,square) ), and ( d(square,square) ). explain the method you used.

Explanation:

Step1: Formula for dilation

When dilating a point \((x,y)\) with respect to a center \((a,b)\) and scale factor \(k\), the formula is \((x',y')=(a + k(x - a),b + k(y - b))\). Since \(A\) is the center of dilation (\(a=-2,b = 3,k = 2\)), for point \(A(-2,3)\):

$$
LATEXBLOCK0
$$

So \(A'(-2,3)\)

Step2: For point \(B(2,3)\)

$$
LATEXBLOCK1
$$

So \(B'(6,3)\)

Step3: For point \(C(5,-2)\)

$$
LATEXBLOCK2
$$

So \(C'(12,-7)\)

Step4: For point \(D(-2,-2)\)

$$
LATEXBLOCK3
$$

So \(D'(-2,-7)\)

Answer:

The coordinates of the image are \(A'(-2,3)\), \(B'(6,3)\), \(C'(12,-7)\), and \(D'(-2,-7)\)