Question

The coordinates of the vertices of a triangle are A(-1, 2), B(3, 1), and C(-3, -2). The coordinates of the vertices of its image are A'(3, -2), B(7, -3), and C'(1, -6). What transformations would result in this image? ΔABC was translated up 4 units and right 4 units. ΔABC was translated up 4 units and left 4 units. ΔABC was translated right 4 units and down 4 units. ΔABC was translated left 4 units and down 4 units.

Answer 1

ΔABC was translated right 4 units and down 4 units.

Explanation:

We know that any transformation of the type:

(x,y) → (x+h,y+k)

is a shift of the figure

h units to the left if h<0

h units to the right if h>0

k units up if k>0

and k units down if k<0

Here,

The coordinates of the original triangle is:

A(-1, 2), B(3, 1), and C(-3, -2).

and that of the translated triangle is:

A'(3, -2), B(7, -3), and C'(1, -6).

i.e. we have:

(-1,2) → (3,-2)

i.e.

(-1+h,2+k)= (3,-2)

i.e.

-1+h= 3 and 2+k= -2

i.e.

h= 3+1 and k= -2-2

i.e.

h=4 and k= -4

This means that ΔABC was shifted 4 units to the right and 4 units down.

( Since, h>0 and k<0 )

Answer 2

ΔABC was translated right 4 units and down 4 units.

Explanation:

A' - A = (3, -2) -(-1, 2) = (3+1, -2-2) = (4, -4)

So, the transformation is (x, y) ⇒ (x +4, y -4).

Adding these values to a coordinate pair causes it to be translated to the right 4 units (x is increased by 4) and down 4 units (y is decreased by 4).