Suppose this parallelogram in the coordinate plane is dilated, with a center of dilation at the origin, using a scale factor of 3. What would be the coordinates of the new vertices E′F′G′H′ (1 point) Responses E′(−3,15), F′(6,24), G′(12,12) and H′(3,3) E′(−3,15), F′(6,24), G′(12,12) and H′(3,3) E′(2,8), F′(5,11), G′(7,7) and H′(4,4) E′(2,8), F′(5,11), G′(7,7) and H′(4,4) E′(−13,53), F′(23,83), G′(43,43) and H′(13,13) E′(−13,53), F′(23,83), G′(43,43) and H′(13,13) E′(−4,2), F′(−1,5), G′(1,1) and H′(−2,−2) E′(−4,2), F′(−1,5), G′(1,1) and H′(−2,−2). F 2,8 E -1,5 G 4,4 H 1,1

Answer 1

To find the coordinates of the new vertices \(E'F'G'H'\) of the parallelogram after dilation with a center at the origin and a scale factor of 3, we need to multiply the coordinates of each vertex by the scale factor.

If the original coordinates of the vertices are:

• \(E(2, 8)\)
• \(F(-1, 5)\)
• \(G(4, 4)\)
• \(H(1, 1)\)

Then, the coordinates after dilation (using the formula \((x, y) \to (kx, ky)\) where \(k\) is the scale factor) will be calculated as follows:

1. \(E' = (3 \cdot 2, 3 \cdot 8) = (6, 24)\)
2. \(F' = (3 \cdot -1, 3 \cdot 5) = (-3, 15)\)
3. \(G' = (3 \cdot 4, 3 \cdot 4) = (12, 12)\)
4. \(H' = (3 \cdot 1, 3 \cdot 1) = (3, 3)\)

So the new vertices after dilation will be:

• \(E'(-3, 15)\)
• \(F'(6, 24)\)
• \(G'(12, 12)\)
• \(H'(3, 3)\)

Thus, the correct response is: E′(−3,15), F′(6,24), G′(12,12) and H′(3,3).