Question

in the following diagram and question, where will point ( c ) go? *
the figure below is dilated by a factor of 3 centered at the origin. image.
click twice to plot a segment.
click a segment to delete it.
( \bigcirc c(6,-1) )
( \bigcirc c(2,-6) )
( \bigcirc c(3,-9) )
( \bigcirc c(9,0) )

Explanation:

Step1: Find the coordinates of point \( C \)

From the graph, the coordinates of point \( C \) are \( (1,-3) \).

Step2: Apply the dilation formula

The formula for dilation centered at the origin with a scale factor \( k \) is \( (x,y)\to(kx,ky) \). Here \( k = 3 \), \( x=1 \), \( y = - 3 \).
Substitute into the formula: \( x'=3\times1=3 \), \( y'=3\times(-3)=-9 \)

Answer:

\( C'(3,-9) \)