The point (5, -7) is dilated by a scale factor of 4 about the origin. Find the location of the new point. Show your work.
New point: (20, -28). Slope of line going through the origin and (5, -7) is -7/5, which makes the radius of that circle sq rt of 74, or
(74)^(1/2). The new radius will be
4*(74)^(1/2). Assuming that the length of the x coordinate (and Y!) is proportional to the radius, that makes the new coordinate (20, -28). Double-checked it with the area of the circle, which increases by a factor of 16 (radius of original circle increased by a factor of 4: r of new circle = 16 times the r of old circle). Let me know if you agree!
To find the new location of the point (5, -7) when dilated by a scale factor of 4 about the origin, we need to multiply both the x-coordinate and the y-coordinate of the point by the scale factor.
Let's start with the x-coordinate:
New x-coordinate = 4 * 5 = 20
Next, let's move on to the y-coordinate:
New y-coordinate = 4 * (-7) = -28
Therefore, the new location of the point (5, -7) when dilated by a scale factor of 4 about the origin is (20, -28).
To find the location of the new point after a dilation, we need to multiply the coordinates of the original point by the scale factor. In this case, the scale factor is 4.
Let's start with the original point (5, -7).
To dilate this point about the origin by a scale factor of 4, we multiply both the x-coordinate and the y-coordinate of the original point by 4.
The new x-coordinate would be: 5 * 4 = 20
The new y-coordinate would be: -7 * 4 = -28
Therefore, the location of the new point after the dilation is (20, -28).
To summarize:
Original point: (5, -7)
Scale factor: 4
New point: (20, -28)