Triangle XYZ is located at X (-2, 1), Y (-4, -3), and Z (0, -2). The triangle is then transformed using the rule (x-1, y+3) to form the image X'Y'Z'. What are the new coordinates of X', Y', and Z'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.

The coordinates of the image points are found by adding (-1, 3) to the coordinates of the original points, as the transformation rule tells you. Then ...

... X' = X + (-1, 3) = (-2-1, 1+3) = (-3, 4)

... Y' = Y + (-1, 3) = (-4-1, -3+3) = (-5, 0)

... Z' = Z + (-1, 3) = (0-1, -2+3) = (-1, 1)

Since each image point is 1 unit to the left and 3 units up from its original, the line segment connecting them will be joining two points that are separated by 1 horizontal unit and 3 vertical units. The line segments will all be parallel (with slope -3) and of the same length (√(1²+3²) = √10).