Question

you do: check for understanding
the line segment cd is dilated with the center of dilation at the origin to obtain a line segment cd. the
coordinates are c(3, -5) and c(6, -10). if the coordinates of d are (x, y), what are the coordinates of
d?
sf(k)=\frac{n}{d}=(kx,ky)
a (x + 2, y + 2)
b (x + 2, 2y)
c (2x, 2y)
d (2x, y)
you do: check for understanding

Explanation:

Step1: Find the scale factor

The formula for dilation with center at the origin is \(SF(k)=\frac{N}{D}\), where \(N\) is the new coordinate and \(D\) is the original coordinate. For point \(C\), original \(x\) - coordinate \(x = 3\) and new \(x\) - coordinate \(x'=6\). So, \(k=\frac{6}{3}=2\).

Step2: Apply the dilation formula

The dilation formula with center at the origin is \((x,y)\to(kx,ky)\). Given the original point \(D(- 5,-10)\), substituting \(k = 2\), \(x=-5\) and \(y = - 10\) into the formula \((kx,ky)\), we get \(x'=2\times(-5)=-10\) and \(y'=2\times(-10)=-20\). But if we consider the general form for any point \((x,y)\) after dilation with scale factor \(k = 2\) (from Step 1) and center at the origin, the rule is \((x,y)\to(2x,2y)\)

Answer:

C. \((2x,2y)\)