The coordinates of the image points are:
M': (-6, 8)
N': (0, 20)
O': (12, -10)
And the measure of angle N' is 48°.
Coordinates of the Image:
Let's find the coordinates of the image points:
Point M:
Original coordinates: (-9, 12)
Scale factor: 2/3
New coordinates: (-9 * 2/3, 12 * 2/3) = (-6, 8)
Image point: M'(-6, 8)
Point N:
Original coordinates: (0, 30)
Scale factor: 2/3
New coordinates: (0 * 2/3, 30 * 2/3) = (0, 20)
Image point: N'(0, 20)
Point O:
Original coordinates: (18, -15)
Scale factor: 2/3
New coordinates: (18 * 2/3, -15 * 2/3) = (12, -10)
Image point: O'(12, -10)
Measure of Angle N':
Dilation preserves angles. This means that the measure of angle N' in the image will be the same as the measure of angle N in the original triangle. Therefore, the measure of angle N' is 48°.
Here's the explanation:
Dilation is a transformation that stretches or shrinks a shape proportionally without changing its angle measures.
Imagine rotating each point of the original triangle around a fixed point (the center of dilation) by the same angle. This rotation will create the image triangle.
Since the angles are rotated by the same amount, their relative positions remain unchanged.
Therefore, the measure of angle N' in the image triangle is the same as the measure of angle N in the original triangle.
In conclusion, the coordinates of the image points are:
M': (-6, 8)
N': (0, 20)
O': (12, -10)
And the measure of angle N' is 48°.