Answer:
and
Step-by-step explanation:
The ratios of sine and cos are defined as follows:
, and
The hypotenuse is always the side opposite of the 90 degree angle (for the given triangle, the hypotenuse is 85)
Since we are looking at the angle A, the opposite side with respect to A would be the side length of 84. That leaves the side 13 as the adjacent side.
Thus, we can now write:
The correct answer is the first answer choice.
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 &
Substituting 6 for x in the equation , we get
.
Dividing 6 on both sides
Simplifying fractions on both sides
Point A from the diagram is (-3, 3)
x-coordinate of A' =
y-coordinate of A' =
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>