For parts a-c, explain what would happen to a figure if you transformed it using the given rule
A) (3x,6y) -
B) (x+2,y+1)-
C) (2x,2y+5)-
A) It's a magnification with stretching. Try to figure out in which direction it stretches.
B) It's a translation. The direction of the translation vector is atan(1/2).
C) It's a magnification (enlargement) followed by a translation in the y axis.
A) If you transformed a figure using the rule (3x, 6y), each x-coordinate would be multiplied by 3 and each y-coordinate would be multiplied by 6. This means that the figure would be scaled horizontally by a factor of 3 and vertically by a factor of 6.
For example, if a point on the original figure has coordinates (1, 2), after the transformation, its coordinates would become (3 * 1, 6 * 2), which is (3, 12).
B) If you transformed a figure using the rule (x+2, y+1), each x-coordinate would be shifted 2 units to the right and each y-coordinate would be shifted 1 unit upwards. This means that the entire figure would be moved 2 units to the right and 1 unit upwards.
For example, if a point on the original figure has coordinates (3, 4), after the transformation, its coordinates would become (3 + 2, 4 + 1), which is (5, 5).
C) If you transformed a figure using the rule (2x, 2y+5), each x-coordinate would be multiplied by 2 and each y-coordinate would be multiplied by 2 and then increased by 5. This means that the entire figure would be scaled horizontally by a factor of 2 and vertically by a factor of 2, and then moved upwards by 5 units.
For example, if a point on the original figure has coordinates (2, 3), after the transformation, its coordinates would become (2 * 2, 2 * 3 + 5), which is (4, 11).