Question

parallelogram jklm has the coordinates j (1, 8), k (12, 8), l (10, 2), and m (-1, 2). which of the following sets of points represents a dilation from the origin of parallelogram jklm?
a. j(4, 11), k(15, 11), l(13, 5), m(2, 5)
b. j(3, 24), k(36, 24), l(30, 6), m(-3, 6)
c. j(1, 24), k(36, 8), l(30, 2), m(-1, 6)
d. j(3, 8), k(36, 8), l(30, 2), m(-3, 2)

Explanation:

Step1: Recall the dilation formula

If a point \((x,y)\) is dilated from the origin by a scale factor \(k\), the new point is \((kx,ky)\).

Step2: Check each option for scale - factor consistency

• Option A:

For \(J(1,8)\) to \(J'(4,11)\), \(x\) - coordinate change: \(4\div1 = 4\), \(y\) - coordinate change: \(11\div8=1.375\). Different scale factors.

• Option B:

For \(J(1,8)\) to \(J'(3,24)\), \(x\) - coordinate change: \(3\div1 = 3\), \(y\) - coordinate change: \(24\div8 = 3\).
For \(K(12,8)\) to \(K'(36,24)\), \(x\) - coordinate change: \(36\div12=3\), \(y\) - coordinate change: \(24\div8 = 3\).
For \(L(10,2)\) to \(L'(30,6)\), \(x\) - coordinate change: \(30\div10 = 3\), \(y\) - coordinate change: \(6\div2=3\).
For \(M(-1,2)\) to \(M'(-3,6)\), \(x\) - coordinate change: \(-3\div(-1)=3\), \(y\) - coordinate change: \(6\div2 = 3\).

• Option C:

For \(J(1,8)\) to \(J'(1,24)\), \(x\) - coordinate change: \(1\div1 = 1\), \(y\) - coordinate change: \(24\div8=3\). Different scale factors.

• Option D:

For \(J(1,8)\) to \(J'(3,8)\), \(x\) - coordinate change: \(3\div1 = 3\), \(y\) - coordinate change: \(8\div8 = 1\). Different scale factors.

Answer:

B. J'(3, 24), K'(36, 24), L'(30, 6), M'(-3, 6)