Question

Write the coordinates of the vertices after a translation 1 unit left and 7 units up.S (6, -10) -> S' (__,__)T (10, -10) -> T' (__,__)U (10, 0) -> U' (__,__)V (6, 0) -> V' (__,__)

Answer 1

To perform a horizontal translation of a point on the coordinate system you have to add/subtract the constant, k, from the x-coordinate of the point:

• If you add the constant, ,x+k,, the resulting translation will be, k units to the right,.

,

• If you subtract the constant, ,x-k,, the resulting translation will be ,k units to the left,.

To perform a vertical translation of a point on the coordinate system, you have to add/subtract a constant, c, from the y-coordinate of the point.

• If you add the constant, ,y+c,, the resulting translation will be, ,c units up.

,

• If you subtract the constant, ,y-c,, the resulting translation will be, c units down.

The points on the coordinate system were moved 1 unit to the left, which means that you have to subtract 1 unit from the x-coordinate of each point and 7 units up, which means that you have to add 7 units to the y-coordinate of each point.

You can express the translation rule as follows:

`(x,y)\to(x-1,y+7)`
`S(6,-10)\to S^(\prime)(6-1,-10+7)=S^(\prime)(5,-3)`
`T(10,-10)\to T^(\prime)(10-1,-10+7)=T^(\prime)(9,-3)`
`U(10,0)\to U^(\prime)(10-1,0+7)=U^(\prime)(9,7)`
`V(6,0)\to V^(\prime)(6-1,0+7)=V^(\prime)(5,7)`

The resulting coordinates after the translation are:

S'(5,-3)

T'(9,-3)

U'(9,7)

V'(5,7)