1).Map. On a map, the coordinates of the corners of a town are A(0.5),B(2,3.5), C(5,1.5), and D(3,1)
The map is dilated so that the perimeter of the town is five times its original perimeter. Find the coordinates of C.
a. (25,7.5)
b. (1,0.3)
c. (25,1.5)
d. (10,6.5)
2).Trangle RST with vertices R(-10,-8),
S(1,7), and T(5,-10) is rotated 90
degrees counterclockwise about the origin Find the coordinate of T.
a. (-5,10)
b. (-10,-5)
c. ((10,5)
d (10,-5)
Get yourself a sheet of graph paper. Plot the corners of the rectangle and of the triangles mentioned.
In (a), see what happens if the coordinates of each rectangle are multiplied by 5. The perimeter becomes 5 times larger while the shape remains the same and the boundary is shorted five times farther from the origin. That will correspond to one of the choices. This may be what they mean by the map being "dilated". I have never heard of that term applied to maps.
In (b), replot the points with the former x coordinate becoming -y and the former y coordinate becoming +x. You shuld see that this is equivalent to a 90 degree rotation of the triangle about the origin. This corrresponds to one of the choices.
If you have a new question, post it separately, not on someone else's thread.
I replotted the points and found the coordinate of T= (-5,10)
The point P has coordinates (-4.1)In which quadrant does point P lie?
1) To solve this problem, we need to understand what it means for the perimeter of the town to be five times its original perimeter. A dilation is a transformation that changes the size of an object without changing its shape.
To find the new coordinates of C, we can use the formula for dilation:
New x-coordinate = Scale factor * Old x-coordinate
New y-coordinate = Scale factor * Old y-coordinate
In this case, the scale factor is 5 (since the perimeter was multiplied by 5). Let's apply the formula to find the new coordinates of C:
New x-coordinate of C = 5 * Old x-coordinate of C = 5 * 5 = 25
New y-coordinate of C = 5 * Old y-coordinate of C = 5 * 1.5 = 7.5
Therefore, the new coordinates of C are (25, 7.5). Option a) (25, 7.5) is the correct answer.
2) To rotate a point counterclockwise about the origin, we can use the following formulas:
New x-coordinate = Old x-coordinate * cos(angle) - Old y-coordinate * sin(angle)
New y-coordinate = Old x-coordinate * sin(angle) + Old y-coordinate * cos(angle)
In this case, the angle of rotation is 90 degrees (π/2 radians). Let's apply the formula to find the new coordinates of T:
New x-coordinate of T = -10 * cos(90 degrees) - (-10) * sin(90 degrees) = 0 - (-10) = 10
New y-coordinate of T = -10 * sin(90 degrees) + (-10) * cos(90 degrees) = -10 + 0 = -10
Therefore, the new coordinates of T are (10, -10). Option d) (10, -5) is the correct answer.