You should know that you can predict changes in coordinates after translations without a graph or anything like that.
(x, y) reflected over the x axis = (x, -y)
(x, y) reflected over the y axis = (-x, y)
(x, y) rotated 90 degrees around the origin = (y, -x)
(x, y) rotated 180 degrees around the origin = (-x, -y)
(x, y) rotated 270 degrees around the origin - (-x, y)
So here's our set of points.
A(1, 2), B(4, 6), C(4, 6)
Here's those points reflected over the x axis.
A'(1, -2), B'(4, -6), C'(4, -6)
And here's <em>those</em> points rotated 180° around the origin.
A''(2, -1), B''(6, -4), C''(6, -4)
I think you made a mistake writing down the question, though, because B and C are the same yet you say ABC forms a triangle. You should be able to go through this process with whatever the coordinate was supposed to be.
If your asking what d equals, then it’s 10
Answer:
A. a = 10
B. m<FNT = 120°
C. m<KTU = 60°
Step-by-step explanation:
A. (7a + 50)° and (14a - 20)° are corresponding angles. Therefore:
(7a + 50)° = (14a - 20)°
Use this equation to find the value of a
7a + 50 = 14a - 20
Combine like terms
7a - 14a = - 50 - 20
-7a = -70
Divide both sides by -7
-7a/-7 = -70/-7
a = 10
B. m<FNT = (14a - 20)° (alternate interior angles are congruent)
Plug in the value of a
m<FNT = 14(10) - 20
m<FNT = 140 - 20
m<FNT = 120°
C. m<KTU + (14a - 20)° = 180° (linear pair)
Plug in the value of a
m<KTU + 14(10) - 20 = 180
m<KTU + 120 = 180
m<KTU + 120 - 120 = 180 - 120
m<KTU = 60°
