Question

The coordinates of the vertices of triangle cde are c (-3, 1), d (-1, 4) and e (-6, 4). a transformation applied to triangle cde creates a congruent triangle sqr. the new coordinates of two vertices are q(-1, 6) and r(-6, 6). what are the coordinates of s?

Answer 1

The coordinates of point s are (-3 , 3)

Explanation:

* Lets revise some transformation

- If the point (x , y) translated horizontally to the right by h units

then the new point = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

then the new point = (x - h , y)

- If the point (x , y) translated vertically up by k units

then the new point = (x , y + k)

- If the point (x , y) translated vertically down by k units

then the new point = (x , y - k)

* Now lets solve the problem

∵ The vertices of triangle cde are c (-3 , 1) , d (-1 , 4) , e (-6 , 4)

∵ The new coordinates of two vertices are q (-1 , 6) , r (-6 , 6)

- The image of point d is q and the image of point e is r

∵ Point d = (-1 , 4) and point q = (-1 , 6)

∵ Point e = (-6 , 4) and point r = (-6 , 6)

- The x-coordinate has no change but the y-coordinate added by 2

∴ The triangle cde translated vertically up by 2 units to create the

congruent triangle sqr

- Lets translate point c two units up to find the coordinates of point s

∵ Point c = (-3 , 1)

∴ Poin s = (-3 , 1 + 2) = -3 , 3)

* The coordinates of point s are (-3 , 3)