Question

problem 4: nys 2038 #19 ng ls.math.content.ny - 8.g.3
figure abcd is shown on the coordinate plane below. the figure will be dilated by a
scale factor of 2 with the center of the dilation at the origin. the resulting image will be
figure abcd
what will be the coordinates of vertex ( a )?
a ( (-5,6) )
b ( (-3,6) )
c ( (-3,8) )
d ( (-6,8) )

Explanation:

Step1: Find the coordinates of point A

From the graph, the coordinates of point \(A\) are \((-3,4)\).

Step2: Apply the dilation formula

The formula for dilation with center at the origin \((0,0)\) and scale factor \(k\) is \((x,y)\to(kx,ky)\). Here \(k = 2\).
Substitute \(x=-3\) and \(y = 4\) into the formula:
\(x'=k\times x=2\times(-3)=-6\)
\(y'=k\times y=2\times4 = 8\)

Answer:

D. \((-6,8)\)