Quadrilateral abcd has vertices a(-3, 4), b(1, 3), c(3, 6), and d(1, 6). match each set of vertices of quadrilateral efgh with the transformation that shows it is congruent to abcd. e(-3, -4), f(1, -3), g(3, -6), and h(1, -6) a translation 7 units right e(-3, -1), f(1, -2), g(3, 1), and h(1, 1) a reflection across the y-axis e(3, 4), f(-1, 3), g(-3, 6), and h(-1, 6) a reflection across the x-axis e(4, 4), f(8, 3), g(10, 6), and h(8, 6) a translation 5 units down

Match: a translation 7 units right = > E(4, 4), F(8, 3), G(10, 6), and H(8, 6)

Match: Reflection across y-axis = > E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

Match: Reflection across x-axis = > E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

Match: a translation 5 unit down = > E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

A) translation 7 unit Right. In this reflection x-coordinate shift 7 unit right.

B) Reflection across y-axis. In this reflection x value change their sign.  

Match: Reflection across y-axis = > E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

C) Reflection across x-axis. In this reflection y value change their sign.

Match: Reflection across x-axis = > E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

D) a translation 5 unit down. In this translation y-coordinate will shift 5 unit down.

Match: a translation 5 unit down = > E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

A translation 7 units right --> E(4, 4), F(8, 3), G(10, 6), and H(8, 6)

Reflection across y-axis   --> E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

Reflection across x-axis   --> E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

A translation 5 unit down --> E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

idn

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240