General Idea:
When we are given a point P(x, y) centered at origin with a scale factor of k, then the dilated point will be given by P' (kx, ky)
Applying the concept:
In the diagram given, the coordinate of C is (6, 3). Triangle ABC is being dilated with the center of dilation at the origin. The image of C, point C' has coordinates of (7.2, 3.6).
If C (x, y) centered at origin with a scale factor of k, then the dilated point will be given by C' (kx, ky)
We know
& ![kx = 7.2](https://tex.z-dn.net/?f=%20kx%20%3D%207.2%20)
Substituting 6 for x in the equation
, we get
.
Dividing 6 on both sides![\frac{6k}{6}=\frac{7.2}{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6k%7D%7B6%7D%3D%5Cfrac%7B7.2%7D%7B6%7D%20%20%20)
Simplifying fractions on both sides![k=1.2](https://tex.z-dn.net/?f=%20k%3D1.2%20)
Point A from the diagram is (-3, 3)
x-coordinate of A' = ![kx=1.2 * -3 = -3.6](https://tex.z-dn.net/?f=%20kx%3D1.2%20%2A%20-3%20%3D%20-3.6%20)
y-coordinate of A' = ![ky =1.2*3=3.6](https://tex.z-dn.net/?f=%20ky%20%3D1.2%2A3%3D3.6%20)
Point A' is given by (-3.6, 3.6)
Conclusion:
<u>Scale factor of dilation is 1.2</u>
<u>The coordinates of point A' is (-3.6, 3.6)</u>