Question

The vertices of a triangle are located at the points A(0, 1), B(2, 4) and C(3, 0). The triangle is translated 5 units down to obtain triangle A′B′C′. What are the coordinates of the vertices of triangle A′B′C

Answer 1

The coordinates of the vertices of triangle A'B'C' are
`A'(x,y) = (0,-4)`,
`B'(x,y) = (2,-1)` and
`C'(x,y) = (3,-5)`.

Explanation:

According to this statement, triangle ABC must be translated 5 units in the -y direction to form triangle A'B'C'. We need to use the following operations:

`A'(x,y) = A(x,y) +(0,-5)` (1)

`B'(x,y) = B(x,y) +(0,-5)` (2)

`C'(x,y) = C(x,y) + (0,-5)` (3)

If we know that
`A(x,y) = (0,1)`,
`B(x,y) = (2,4)` and
`C(x,y) = (3,0)`, then the new vertices of the rectangle are, respectively:

`A'(x,y) = (0,-4)`,
`B'(x,y) = (2,-1)`,
`C'(x,y) = (3,-5)`