he vertices of a figure are given. Find the coordinates of the figure after the transformations given.
F(−9,−9),G(−3,−6),H(−3,−9)
Dilate with respect to the origin using a scale factor of 23. Then translate 6 units up.
DISCLAMER Not an answer, just a comment, I HATE MATH, Which is why I tried getting help..… I did not find any, just how to write 2/3
To dilate a figure with respect to the origin using a scale factor of 23, you need to multiply the coordinates of each vertex by the scale factor.
So, let's apply the dilation to the given coordinates of the vertices:
F' = (−9 * 23, −9 * 23) = (−207, −207)
G' = (−3 * 23, −6 * 23) = (−69, −138)
H' = (−3 * 23, −9 * 23) = (−69, −207)
Now, to translate the figure 6 units up, you need to add 6 to the y-coordinate of each vertex:
F'' = (−207, −207 + 6) = (−207, −201)
G'' = (−69, −138 + 6) = (−69, −132)
H'' = (−69, −207 + 6) = (−69, −201)
Therefore, after the given transformations, the new coordinates of the figure are:
F''(−207, −201)
G''(−69, −132)
H''(−69, −201)
To find the coordinates of the figure after the dilations and translation, we need to apply each transformation step by step.
1. Dilation with respect to the origin using a scale factor of 23:
To dilate a point with respect to the origin, we multiply both the x-coordinate and the y-coordinate by the scale factor.
For point F(-9, -9):
x-coordinate after dilation = (-9) * 23 = -207
y-coordinate after dilation = (-9) * 23 = -207
So, the coordinates of F after the dilation are (-207, -207).
For point G(-3, -6):
x-coordinate after dilation = (-3) * 23 = -69
y-coordinate after dilation = (-6) * 23 = -138
Therefore, the coordinates of G after the dilation are (-69, -138).
For point H(-3, -9):
x-coordinate after dilation = (-3) * 23 = -69
y-coordinate after dilation = (-9) * 23 = -207
Thus, the coordinates of H after the dilation are (-69, -207).
2. Translation 6 units up:
To translate a point vertically, we add the translation distance to the y-coordinate.
For point F after dilation (-207, -207):
y-coordinate after translation = -207 + 6 = -201
The coordinates of F after the dilation and translation are (-207, -201).
For point G after dilation (-69, -138):
y-coordinate after translation = -138 + 6 = -132
Therefore, the coordinates of G after the dilation and translation are (-69, -132).
For point H after dilation (-69, -207):
y-coordinate after translation = -207 + 6 = -201
Hence, the coordinates of H after the dilation and translation are (-69, -201).
In conclusion, after the dilation with a scale factor of 23 and the translation 6 units up, the new coordinates of the figure are:
F': (-207, -201), G': (-69, -132), H': (-69, -201).
multiply all the coordinates by 23 (or, fix your typo first)
Then add 6 to all the y values