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coordinates on a map e4q15 *
- Thread starter tamiatha
- Start date
Re: coordinates on a map e4q15
Did you find the perimeter of the first map ?tamiatha said:on a map, the coordinates of the corners of a town are:
A(0.5,2)
B(2,3.5)
C(5,1.5)
D(3,1)
the map is dilated so that the perimeter of the town is 5 times its original perimeter. Find the coordinates of C.
D
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Re: coordinates on a map e4q15
What is the shape of the town?
When the perimeter is doubled - by how much the length of the each side is increased?
Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
tamiatha said:on a map, the coordinates of the corners of a town are:
A(0.5,2)
B(2,3.5)
C(5,1.5)
D(3,1)
the map is dilated so that the perimeter of the town is 5 times its original perimeter. Find the coordinates of C.
What is the shape of the town?
When the perimeter is doubled - by how much the length of the each side is increased?
Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
Re: coordinates on a map e4q15
If the perimeter of the image is 5 times the perimeter of the original figure, then the length of each side in the image will be 5 times as big as the length of the corresponding side in the original figure.
If S is a dilation with magnitude k, and P(x, y) is a point to which the dilation is applied, the image of P (called P') is (kx, ky). If you apply dilation S to two points, P and Q, the distance between the images P' and Q' is k times the distance between the original points P and Q. That is, P'Q' = k*PQ.
So....if you want the sides of A'B'C'D' to be 5 times as long as the sides of ABCD (which would give you a perimeter 5 times as large), then the magnitude of the dilation must be 5.
I'll find the coordinates of point A, and leave it to you to find the coordinates of point C.
If we apply a dilation of magnitude 5 to the point A(0.5, 2), the IMAGE of A will be A'(5*0.5, 5*2), or (2.5, 10)
tamiatha said:on a map, the coordinates of the corners of a town are:
A(0.5,2)
B(2,3.5)
C(5,1.5)
D(3,1)
the map is dilated so that the perimeter of the town is 5 times its original perimeter. Find the coordinates of C.
If the perimeter of the image is 5 times the perimeter of the original figure, then the length of each side in the image will be 5 times as big as the length of the corresponding side in the original figure.
If S is a dilation with magnitude k, and P(x, y) is a point to which the dilation is applied, the image of P (called P') is (kx, ky). If you apply dilation S to two points, P and Q, the distance between the images P' and Q' is k times the distance between the original points P and Q. That is, P'Q' = k*PQ.
So....if you want the sides of A'B'C'D' to be 5 times as long as the sides of ABCD (which would give you a perimeter 5 times as large), then the magnitude of the dilation must be 5.
I'll find the coordinates of point A, and leave it to you to find the coordinates of point C.
If we apply a dilation of magnitude 5 to the point A(0.5, 2), the IMAGE of A will be A'(5*0.5, 5*2), or (2.5, 10)