4. The shortest distance between point W and a line of reflection is 64 inches.What will be the distance between W and its image W'?
A) 8in B) 32 in
C) 64 in D) 128 in
5 Brayton is going to rotate point X (8, -3) 90 degrees counterclockwise about point Y (3,2). What are the coordinates of X'
A. X' (8,7)
B. X' (-2,-3)
C. X' (-3,8)
D. X' (-8,-7)
A) 8in B) 32 in
C) 64 in D) 128 in
5 Brayton is going to rotate point X (8, -3) 90 degrees counterclockwise about point Y (3,2). What are the coordinates of X'
A. X' (8,7)
B. X' (-2,-3)
C. X' (-3,8)
D. X' (-8,-7)
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4. If it's 64 inches between W and the mirror (line of reflection), then there's 64 inches "inside" the mirror to the reflected W, which is W'. Therefore the distance between W and W' is 64+64 = 128 inches. So D.
5. Frankly, I'd draw this up, do the rotation, and approximate it. The nice thing about this question is that the four answers are in the four different quadrants!
Since the start point is in quadrant 4, and the rotation point is in quadrant 1, a rotation counterclockwise will move the start point into quadrant 1.
The only quadrant 1 answer is X' (8,7), which is what my drawing approximation shows... so the answer is A).
If you have to do it on paper, you'd need to do the following:
1) Calculate the distance between the two points
2) Find the slope of the line XY
3) Get the negative inverse slope, which is the slope after 90° has been applied
4) Find the equation of the line passing through Y with the new slope
5) Find the two points on the line that are the calculated distance from point Y
6) Eliminate one of the two points.
5. Frankly, I'd draw this up, do the rotation, and approximate it. The nice thing about this question is that the four answers are in the four different quadrants!
Since the start point is in quadrant 4, and the rotation point is in quadrant 1, a rotation counterclockwise will move the start point into quadrant 1.
The only quadrant 1 answer is X' (8,7), which is what my drawing approximation shows... so the answer is A).
If you have to do it on paper, you'd need to do the following:
1) Calculate the distance between the two points
2) Find the slope of the line XY
3) Get the negative inverse slope, which is the slope after 90° has been applied
4) Find the equation of the line passing through Y with the new slope
5) Find the two points on the line that are the calculated distance from point Y
6) Eliminate one of the two points.
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4. The shortest distance between point W and a line of reflection is 64 inches.What will be the distance between W and its image W'?
It will be twice the distance from the point to the line so D is the answer.
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5 Brayton is going to rotate point X (8, -3) 90 degrees counterclockwise about point Y (3,2). What are the coordinates of X'
Point X is in quadrant 4;
Point Y is in quadrant 1 and is closer to the origin than point X;
if you rotate X about Y 90 degrees counter clockwise, then X' should be in quadrant 1. Only point A is in quadrant 1 so the answer is A.
It will be twice the distance from the point to the line so D is the answer.
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5 Brayton is going to rotate point X (8, -3) 90 degrees counterclockwise about point Y (3,2). What are the coordinates of X'
Point X is in quadrant 4;
Point Y is in quadrant 1 and is closer to the origin than point X;
if you rotate X about Y 90 degrees counter clockwise, then X' should be in quadrant 1. Only point A is in quadrant 1 so the answer is A.