Answer
a) The vertices of the triangle after the transformation is
A' (1, -4)
B' (5, -1)
C' (4, -4)
b)
Explanation
When a coordinate A(x, y) is translated horizontally along the x-axis by a units, the new coordinates, A'(x', y') is represented as
A[(x + a), y] when the translation is by a units to the right.
A[(x - a), y] when the translation is by a units to the left.
When a coordinate A(x, y) is translated vertically along the y-axis by b units, the new coordinates, A'(x', y') is represented as
A' [x, (y + b)] when the translation is by b units upwards.
A [x, (y - b)] when the translation is by b units downwards.
So, a movement of the cordinates of the triangle 3 units to the right and 5 units down will add 3 units to the x-coordinate and subtract 5 units from the y-coordinates
A (-2, 1) = A' [(-2 + 3), (1 - 5)] = A' (1, -4)
B (2, 4) = B' [(2 + 3), (4 - 5)] = B' (5, -1)
C (1, 1) = C' [(1 + 3), (1 - 5)] = C' (4, -4)
b) To graph the two triangles, we just plot the coordinates of the vertices and connect them. This is presented under 'Answer' above.
Hope this Helps!!!
