If triangle R'S'T' is a dilation of triangle RST, what would be the rest of the coordinates for triangle R'S'T?
R (-2,-3)
S (0,2)
T (2,-3)
R'(-6,-9)
S'( , )
T' ( , )
A dilation is basically the opposite of a contraction. So you can see that the first coordinate pair has increased by a factor of 3 from one triangle to the next. Therefore, do the same to the other coordinate pairs.
S'(0*3,2*3) = (0,6)
T'(2*3,-3*3) = (6,-9)
Hope this helps!
Manny
thank you!
To find the rest of the coordinates for triangle R'S'T', we need to determine the dilation factor. A dilation is a transformation that changes the size of a figure without changing its shape. In this case, triangle R'S'T' is a dilation of triangle RST.
To find the dilation factor, we can compare the corresponding side lengths of the two triangles. Let's take the distance between R and R', which is 4 units. The distance between S and S' is also 4 units. Therefore, the dilation factor is 4.
Given the coordinates of point R (-2, -3) and R' (-6, -9), we can apply the dilation factor to find the coordinates of S' and T'.
To find S':
The x-coordinate of S' is obtained by multiplying the x-coordinate of S by the dilation factor (4) and subtracting it from the x-coordinate of R'.
x-coordinate of S' = dilation factor * x-coordinate of S + x-coordinate of R'
= 4 * 0 + (-6) = -6
Therefore, S' has coordinates (-6, y).
The y-coordinate of S' is obtained by multiplying the y-coordinate of S by the dilation factor (4) and subtracting it from the y-coordinate of R'.
y-coordinate of S' = dilation factor * y-coordinate of S + y-coordinate of R'
= 4 * 2 + (-9) = -1
Therefore, S' has coordinates (-6, -1).
To find T':
Using the same process, we can find the coordinates of T'.
The x-coordinate of T':
x-coordinate of T' = dilation factor * x-coordinate of T + x-coordinate of R'
= 4 * 2 + (-6) = 2
Therefore, T' has coordinates (2, y).
The y-coordinate of T':
y-coordinate of T' = dilation factor * y-coordinate of T + y-coordinate of R'
= 4 * (-3) + (-9) = -21
Therefore, T' has coordinates (2, -21).
Therefore, the missing coordinates for triangle R'S'T' are:
R'(-6, -9)
S'(-6, -1)
T'(2, -21)
To find the coordinates of triangle R'S'T', we'll use the concept of dilation. A dilation is a transformation that changes the size of a figure but keeps the shape intact. It involves multiplying the coordinates of each point by a scaling factor.
In this case, triangle R'S'T' is a dilation of triangle RST. To find the scaling factor, we can compare the corresponding sides of both triangles. Since R' is at (-6,-9) and R is at (-2,-3), we can see that the x-coordinate of R' is 3 times smaller than the x-coordinate of R, and the y-coordinate of R' is 3 times smaller than the y-coordinate of R.
Therefore, the scaling factor is 3. To find the rest of the coordinates for triangle R'S'T', we'll multiply the coordinates of S and T by 3:
S' = (0 * 3, 2 * 3) = (0, 6)
T' = (2 * 3, -3 * 3) = (6, -9)
So, the coordinates for triangle R'S'T' are:
R'(-6,-9)
S'(0,6)
T'(6,-9)