Question

Segment EF has coordinates E(0, 2) and F(1, -4). Segment EF is translated using the translation rule (x, y) ⟶ (x + 5, y + 4) to map onto segment E'F'. Segment E'F' is translated using the translation rule (x, y) ⟶ (x - 2, y - 1) to map onto segment E''F''. What are the coordinates of segment E''F''?

Answer 1

Given:

Segment EF has coordinates E(0, 2) and F(1, -4).

Segment EF is translated using the translation rule (x, y) ⟶ (x + 5, y + 4) to map onto segment E'F'.

Segment E'F' is translated using the translation rule (x, y) ⟶ (x - 2, y - 1) to map onto segment E''F''.

To find:

The coordinates of segment E''F''.

Solution:

Segment EF has coordinates E(0, 2) and F(1, -4).

Segment EF is translated using the translation rule (x, y) ⟶ (x + 5, y + 4) to map onto segment E'F'.

$E(0,2)\to E'(0+5,2+4)=E'(5,6)$

$F(1,-4)\to F'(1+5,-4+4)=F'(6,0)$

Segment E'F' is translated using the translation rule (x, y) ⟶ (x - 2, y - 1) to map onto segment E''F''.

$E'(5,6)\to E''(5-2,6-1)=E''(3,5)$

$F'(6,0)\to F''(6-2,0-1)=F''(4,-1)$

Therefore, the coordinates of the segment E''F'' are E''(3,5) and F''(4,-1).