ΔABC is reflected across the x-axis and then translated 4 units up to create ΔA′B′C′. What are the coordinates of the vertices of ΔA′B′C′ ? A.
A′(-3, 3), B′(-1, 1), C′(-2, 3)

B.
A′(3, -3), B′(1, -1), C′(2, -3)

C.
A′(3, -5), B′(1, -7), C′(3, -5)

D.
A′(-3, 3), B′(-1, 1), C′(-2, -3)

The missing figure is attached down

The coordinates of the vertices of Δ A'B'C' are A' (-3, 3), B' (-1, 1), C' (-2, 3) ⇒ A

Step-by-step explanation:

If the point (x, y) reflected across the x-axis , then its image is (x, -y)

If the point (x, y) translated vertically up by k units then its image is (x, y + k)

Let us solve the question using the rules above

∵ The coordinates of Δ ABC are A (-3, 1), B (-1, 3), C = (-2, 1)

∵ Δ ABC reflected across the x-axis at first

→ By using the first rule above change the signs of y coordinates

∴ The image of A = (-3, -1)

∴ The image of B = (-1, -3)

∴ The image of C = (-2, -1)

∵ Then it translated 4 units up

→ Use the second rule above, where k = 4, add each y-coordinates by 4

∴ A' = (-3, -1 + 4)

∴ A' = (-3, 3)

∴ B' = (-1, -3 + 4)

∴ B' = (-1, 1)

∴ C' = (-2, -1 + 4)

∴ C' = (-2, 3)

The coordinates of the vertices of Δ A'B'C' are A' (-3, 3), B' (-1, 1), C' (-2, 3)

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841