Triangle TUV is mapped onto T'U'V' by a dilation with a scale factor of 1/2 and center (2,-3) followed by a reflection over the x axis what are the coordiantes of T'U'V"
hard to say, without knowing T,U,V
2/5
Let's start by finding the coordinates of each point after the dilation with a scale factor of 1/2 and center (2,-3):
To dilate a point (x, y) with a scale factor of 1/2 and center (h, k), you can use the following formulas:
x' = h + (1/2)(x - h)
y' = k + (1/2)(y - k)
For point T( x_1, y_1), we have:
x'_1 = 2 + (1/2)(x_1 - 2)
y'_1 = -3 + (1/2)(y_1 - (-3))
Now, let's find the coordinates of each point after the reflection over the x-axis. The reflection over the x-axis simply changes the sign of the y-coordinate. Therefore, the new coordinates (x", y") after the reflection can be found as:
x" = x'
y" = -y'
For point T', we have:
x" = x'_1
y" = -y'_1
Similarly, you can find the coordinates for points U' and V' using the above formulas.
To find the coordinates of T'U'V' after the given transformations (dilation and reflection over the x-axis), we first need to apply the dilation and then the reflection.
1. Dilation with a scale factor of 1/2 and center (2, -3):
- For each vertex of the original triangle TUV, we need to multiply its distance from the center by the scale factor (1/2).
Let's say the coordinates of T, U, and V are (xT, yT), (xU, yU), and (xV, yV) respectively. The coordinates of the center (2, -3) will remain the same.
The dilation formulas for each vertex are:
- xT' = (xT - 2) * (1/2) + 2
- yT' = (yT + 3) * (1/2) - 3
- xU' = (xU - 2) * (1/2) + 2
- yU' = (yU + 3) * (1/2) - 3
- xV' = (xV - 2) * (1/2) + 2
- yV' = (yV + 3) * (1/2) - 3
2. Reflection over the x-axis:
- To reflect a point over the x-axis, we only need to change the sign of its y-coordinate.
The reflection formulas for each vertex are:
- xT" = xT'
- yT" = -yT'
- xU" = xU'
- yU" = -yU'
- xV" = xV'
- yV" = -yV'
Therefore, the coordinates of T'U'V" after the given transformations are (xT", yT"), (xU", yU"), and (xV", yV") respectively.
Note: You can substitute the coordinates of T, U, and V into the formulas to calculate the exact values.