Question

The police department now needs you to take the original triangle and reflect it. For this step, you will need to identify and label three points on the coordinate plane that are a reflection of the original triangle. Next, use the coordinates of your reflection to show that the two triangles are congruent by the ASA postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge. You must show all work with the distance formula for the corresponding sides and angles.

Answer 1

I reflected it already. i just need the second part. PLEASE HELP i've been stuck on this the entire day....

Answer 2

@Zarkon @mathmate

Answer 3

@thomaster @jim_thompson5910

Answer 4

Are you allowed to use trigonometry?

Answer 5

yeah. @jim_thompson5910

Answer 6

are you familiar with sine, cosine, tangent, etc?

Answer 7

No :/

Answer 8

Say we had this right triangle (with angle theta)

Answer 9

now let's say we had these side lengths

Answer 10

we can set up these equations


sin(theta) = opposite/hypotenuse = 3/5
sin(theta) = 3/5

cos(theta) = adjacent/hypotenuse = 4/5
cos(theta) = 4/5

tan(theta) = opposite/adjacent = 3/4
tan(theta) = 3/4

Answer 11

sound familiar?

Answer 12

yes!

Answer 13

so let's say we focus on

sin(theta) = 3/5

Answer 14

to isolate theta, we apply the arcsine function to both sides

sin(theta) = 3/5

arcsin( sin(theta) ) = arcsin(3/5)

theta = arcsin(3/5)

theta = 36.8698976

So the angle theta is roughly 36.8698976 degrees

Answer 15

You can use this idea to solve for the angles of your triangle