Question

A sequence of translations maps ∆ABC to ∆A’B’C’.

∆ABC has vertices A(-3, 4), B(-3, 0), C(-1, 3)
The coordinates for A’ are (3, -4)


(a) What is the coordinate rule that maps ∆ABC onto ∆A’B’C’?


(b) What are the coordinates for B’ and C’?

Answer 1

(a) Co-ordinate rule is
`x'=x+6` and
`y'=y-8`

(b) Co-ordinates of B' and C' are
`(3,-8)` and
`(5,-5)` respectively.

Explanation:

(a)

Here, the co-ordinates of A
`(-3,4)` are translated to A'
`(3,-4)`.

For the co-ordinates A and A',
`x'-x=3-(-3)=3+3=6` and
`y'-y=-4-4=-8`

So, x value of A has shifted to right by 6 units and y value of A has shifted 8 units down.

Hence, the co-ordinate rule that maps ΔABC onto ΔA'B'C' is:

`x'=x+6` and
`y'=y-8`.

(b)

Using the co-ordinate rule, we can find the co-ordinates of B' and C'.

For B,
`x=-3` and
`y=0`.

So,
`x'` of B' is
`x'=x+6=-3+6=3`

And,
`y'` of B' is
`y'=y-8=0-8=-8`.

Therefore, co-ordinates of B' are
`(3,-8)`.

For C,
`x=-1` and
`y=3`.

So,
`x'` of C' is
`x'=x+6=-1+6=5`

And,
`y'` of C' is
`y'=y-8=3-8=-5`.

Therefore, co-ordinates of C' are
`(5,-5)`.