A figure has a vertices (-13,13),(26,52),(39,39), what would be The new coordinates of the vertices To the nearest tenth if the image were reduced by scale factor of 0.77 with the origin as the center of dilation
just multiply each coordinate by 0.77
Well, it seems like this figure is going through a shrinkage therapy! Let's see how it transforms.
To find the new coordinates after reducing the image by a scale factor of 0.77 with the origin as the center of dilation, we'll multiply the x and y values of each vertex by 0.77.
Starting with (-13, 13):
New x-coordinate: -13 * 0.77 = -10.01 (rounded to the nearest tenth)
New y-coordinate: 13 * 0.77 = 10.01 (rounded to the nearest tenth)
Moving on to (26, 52):
New x-coordinate: 26 * 0.77 = 20.02 (rounded to the nearest tenth)
New y-coordinate: 52 * 0.77 = 40.04 (rounded to the nearest tenth)
And lastly, (39, 39):
New x-coordinate: 39 * 0.77 = 30.03 (rounded to the nearest tenth)
New y-coordinate: 39 * 0.77 = 30.03 (rounded to the nearest tenth)
So, the new coordinates of the vertices to the nearest tenth are:
(-10.0, 10.0), (20.0, 40.0), and (30.0, 30.0).
Hope these coordinates provided a little laughter for your geometric journey!
To find the new coordinates of the vertices after the figure is reduced by a scale factor of 0.77 with the origin as the center of dilation, you can multiply the original coordinates by the scale factor.
Let's calculate the new coordinates for each vertex:
Vertex A: (-13, 13)
New x-coordinate: -13 * 0.77 ≈ -10.0
New y-coordinate: 13 * 0.77 ≈ 10.0
New coordinates for vertex A: (-10.0, 10.0)
Vertex B: (26, 52)
New x-coordinate: 26 * 0.77 ≈ 20.0
New y-coordinate: 52 * 0.77 ≈ 40.0
New coordinates for vertex B: (20.0, 40.0)
Vertex C: (39, 39)
New x-coordinate: 39 * 0.77 ≈ 30.0
New y-coordinate: 39 * 0.77 ≈ 30.0
New coordinates for vertex C: (30.0, 30.0)
Therefore, the new coordinates of the vertices to the nearest tenth would be:
Vertex A: (-10.0, 10.0)
Vertex B: (20.0, 40.0)
Vertex C: (30.0, 30.0)
To find the new coordinates of the vertices after the figure is reduced by a scale factor of 0.77 with the origin as the center of dilation, you can follow these steps:
1. Find the distance from the origin to each vertex of the original figure.
The distance from the origin to a point (x, y) can be calculated using the distance formula:
distance = sqrt(x^2 + y^2)
For the given vertices:
Distance from origin to (-13, 13) = sqrt((-13)^2 + 13^2) = sqrt(338)
Distance from origin to (26, 52) = sqrt(26^2 + 52^2) = sqrt(3380)
Distance from origin to (39, 39) = sqrt(39^2 + 39^2) = sqrt(3042)
2. Multiply each distance by the scale factor of 0.77 to find the new distances.
New distance = scale factor * old distance
New distance from origin to (-13, 13) = 0.77 * sqrt(338) = 7.34
New distance from origin to (26, 52) = 0.77 * sqrt(3380) = 42.89
New distance from origin to (39, 39) = 0.77 * sqrt(3042) = 35.18
3. Calculate the angle from the origin to each vertex using trigonometry.
The angle from the origin to a point (x, y) can be calculated as:
angle = atan(y / x)
For the given vertices:
Angle from origin to (-13, 13) = atan(13 / -13) = -45 degrees
Angle from origin to (26, 52) = atan(52 / 26) = 63.4 degrees
Angle from origin to (39, 39) = atan(39 / 39) = 45 degrees
4. Use the new distances and angles to find the new coordinates of each vertex.
The new coordinates (x', y') can be calculated as:
x' = new distance * cos(angle)
y' = new distance * sin(angle)
For (-13, 13):
x' = 7.34 * cos(-45 degrees) = 5.195
y' = 7.34 * sin(-45 degrees) = -5.195
For (26, 52):
x' = 42.89 * cos(63.4 degrees) = 17.913
y' = 42.89 * sin(63.4 degrees) = 37.811
For (39, 39):
x' = 35.18 * cos(45 degrees) = 24.853
y' = 35.18 * sin(45 degrees) = 24.853
Therefore, the new coordinates of the vertices (rounded to the nearest tenth) after the figure is reduced by a scale factor of 0.77 with the origin as the center of dilation are:
(-13, 13) -> (5.2, -5.2)
(26, 52) -> (17.9, 37.8)
(39, 39) -> (24.9, 24.9)