What are the new vertices of triangle ABC, shown, if the triangle is translated two units upward? Question 4 options: A) A′ = (–5,–2), B′ = (–1,4), C′ = (4,–2)
B) A′ = (–3,–5), B′ = (1,1), C′ = (6,–5)
C) A′ = (–5,–4), B′ = (–1,2), C′ = (4,–4)
D) A′ = (–5,–3), B′ = (–1,3), C′ = (4,–3)

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step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

not sure but it may be b, as i said i'm not sure.

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)