Question

TIME REMAINING

51:59
On a coordinate plane, 2 triangles are shown. Triangle D E F has points (6, 4), (5, 8) and (1, 2). Triangle R S U has points (negative 2, 4), (negative 3, 0), and (2, negative 2).

Triangle DEF is reflected over the y-axis, and then translated down 4 units and right 3 units. Which congruency statement describes the figures?

ΔDEF ≅ ΔSUR
ΔDEF ≅ ΔSRU
ΔDEF ≅ ΔRSU
ΔDEF ≅ ΔRUS

Answer 1

ΔDEF ≅ ΔSRU

Explanation:

The answer above is correct.

Answer 2

(b) ΔDEF ≅ ΔSRU

Explanation:

Given point coordinates D(6, 4), E(5, 8), F(1, 2), you want the congruence statement for ∆DEF, given points R(-2, 4), S(-3, 0), U(2, -2) and the fact that ∆DEF is reflected across the y-axis and translated (3, -4).

Graph

The attached graph plots the given points. It is pretty clear that corresponding vertices are (D, S), (E, R), (F, U).

∆DEF ≅ ∆SRU

Transformation

Reflection across the y-axis is described by ...

(x, y) ⇒ (-x, y)

Translation right 3 and down 4 is described by ...

(x, y) ⇒ (x +3, y -4)

Taken together, the transformation is ...

(x, y) ⇒ (-x +3, y -4)

Applied to points D, E, F, we have ...

D(6, 4) ⇒ D'(-3, 0) . . . . matches S

E(5, 8) ⇒ E'(-2, 4) . . . . matches R

These two matches are sufficient to tell us that point F will be transformed to point U, and the congruence statement is ...

∆DEF ≅ ∆SRU