A coordinate plane's x-axis ranges from negative 6 to 2 and its y-axis ranges from negative 3 to 2, both by 1-unit increments. 4 points forming a parallelogram are plotted, labeled upper A, upper B, upper C, and upper D, respectively.
Suppose parallelogram ABCD is dilated using a magnitude of 2 and a center of dilation at (−2,−1) . What would be the corresponding ordered pair at point A ?
(1 point)
Responses
(−5,0)
left parenthesis negative 5 comma 0 right parenthesis
(−4,3)
left parenthesis negative 4 comma negative 3 right parenthesis
(−1,2)
left parenthesis negative 1 comma 2 right parenthesis
(−3,0)
To find the corresponding ordered pair at point A after the dilation, we can use the formula for dilation:
(x', y') = (h + k(x - h), k(y - k)),
where (h, k) is the center of dilation and (x, y) are the original coordinates of point A.
In this case, the center of dilation is (-2, -1), the original coordinates of point A are (-6, 2), and the magnitude of dilation is 2. Plugging these values into the formula, we get:
(x', y') = (-2 + 2(-6 - (-2)), -1 + 2(2 - (-1)))
= (-2 + 2(-6 + 2), -1 + 2(2 + 1))
= (-2 + 2(-4), -1 + 2(3))
= (-2 - 8, -1 + 6)
= (-10, 5)
Therefore, the corresponding ordered pair at point A after the dilation is (-10, 5).
None of the given options match this answer, so none of the given options are correct.