A (0,0)

Question

B (1,-3)
C (3,0)

Find the coordinates of point C' by dilating triangle ABC by a scale factor of 2 with a center of dilation at the origin. Enter your response as an ordered pair.

Point C' is at (_,_)

Answer 1

To find the coordinates of point C' after dilating triangle ABC by a scale factor of 2 with a center of dilation at the origin, we apply the following rule for dilation:

If a point $(x,y)$ is dilated from the origin by a scale factor $k$, the new coordinates $(x^{\prime },y^{\prime })$ after dilation are given by: $$(x^{\prime },y^{\prime })=(kx,ky)$$

In this case, the coordinates of point C are $C(3,0)$ and the scale factor $k$ is 2. Thus, we have:

$$C^{\prime }(x^{\prime },y^{\prime })=(2\cdot 3,2\cdot 0)=(6,0)$$

Therefore, the coordinates of point C' are $(6,0)$.

So, the answer is: Point C' is at $(6,0)$.