Triangle ABC has vertices point A(−2,−2) , point B(−4,−3) , and point C(−2,−5) . Find the coordinates of A′ , B′ , and C′ after a dilation with a scale factor of 3 and a center point of dilation at the origin.(

Answer 1

To find the coordinates of the points A', B', and C' after a dilation with a scale factor of 3 and a center of dilation at the origin, we can use the formula for dilation:

$$(x^{\prime },y^{\prime })=(k\cdot x,k\cdot y)$$

where $(x,y)$ are the original coordinates of the point, $(x^{\prime },y^{\prime })$ are the coordinates after dilation, and $k$ is the scale factor.

Given the original points:

• A(-2, -2)
• B(-4, -3)
• C(-2, -5)

We will apply the dilation to each of these points with $k=3$.

For Point A(-2, -2):

$$A^{\prime }=(3\cdot -2,3\cdot -2)=(-6,-6)$$

For Point B(-4, -3):

$$B^{\prime }=(3\cdot -4,3\cdot -3)=(-12,-9)$$

For Point C(-2, -5):

$$C^{\prime }=(3\cdot -2,3\cdot -5)=(-6,-15)$$

Summary of Transformed Points:

• $A^{\prime }=(-6,-6)$
• $B^{\prime }=(-12,-9)$
• $C^{\prime }=(-6,-15)$

Thus, the coordinates of the points after dilation are:

• A'(-6, -6)
• B'(-12, -9)
• C'(-6, -15)