A type of transformation that occurs when a figure is moved from one location to another on the coordinate plane without changing its size, shape or orientation is a translation. Matrix addition can be used to find the coordinates of the translated figure.
Find the coordinates of the vertices of triangle TRI with T(2, –1), R(4, 3), and I(–3, –2) if it is to be moved 5 units to the left and 2 units up.
Write the coordinates of the triangle as a coordinate matrix.
Translating the triangle 5 units to the left means that each x-coordinate decreases by 5.
Translating the triangle 2 units up means that each y-coordinate increases by 2.
The translation matrix that will do this is
To find the coordinates of the vertices of the translated triangle T'R'I ' add the translation matrix to the coordinate matrix:
The coordinates of the vertices of T'R'I ' are T '(–3, 1), R'(–1, 5) and I'(–8, 0).