Question

41) Triangle CAT has vertices

C(-9,9), A(-3,3), and T(-6,0). If ABUG has vertices B(-3,3), U(-1, 1), and
G(-2,0). Is ACAT similar to ABUG? If so, what transformation maps ACAT onto ABUG?

A. No, dilation centered at the origin with scale factor of 3.
B. No, dilation centered at the origin with scale factor of
C. Yes, dilation centered at the origin with scale factor of 3.
D. Yes, dilation centered at the origin with scale factor of

Answer 1

Answer: yes

Step-by-step explanation THE Answer the length of the median

is 11.4 units.

Step 1. Given Information.

Given triangle CAT has vertices

,

and

. M is the midpoint of

.

The length of the median

is to be determined.

Step 2. Explanation.

The midpoint of two points

is given by

.

Plugging the values in the equation to find the point M:

The distance between two points

is given by

.

Plugging the given values in the equation to find the distance between C and M:

Step 3. Conclusion.

Hence, the length of the median

is 11.4 units.

Answer 2

Answer: Yes, dilation centered at the origin with scale factor of 3.

Explanation:

Two figures are similar if they have the same shape, but possibly different sizes. In order to check whether two triangles are similar, we need to check whether their corresponding angles are congruent and whether their corresponding side lengths are proportional.

We can see that triangle ACAT and triangle ABUG have corresponding angles that are congruent, and their corresponding side lengths are proportional with a ratio of 3 (i.e., AC = 3AB, AT = 3AU, and CT = 3UG). Therefore, triangle ACAT is similar to triangle ABUG.

To map triangle ACAT onto triangle ABUG, we need a transformation that scales each point by a factor of 3 about the origin (since the dilation is centered at the origin). Therefore, the correct answer is option (C).