graph triangle rst with vertices r(-1,3),s(4,-2), t(2,-5)
Draw the image triangle r's't' formed by rotating triangle rst 90 degree, 180 degrees, and 270 degrees about the origin. Give the coordinates of r',s', and t'.
To draw the image triangle, we need to apply the rotation transformation to each vertex of the original triangle. The rotation is centered at the origin.
Let's start with the 90-degree rotation. To rotate a point (x, y) 90 degrees counterclockwise, we can use the formulas:
x' = -y
y' = x
Now, let's apply this formula to each vertex of triangle RST:
For vertex R(-1, 3):
x' = -3
y' = -1
So, the coordinates of R' are (-3, -1).
For vertex S(4, -2):
x' = 2
y' = 4
So, the coordinates of S' are (2, 4).
For vertex T(2, -5):
x' = 5
y' = -2
So, the coordinates of T' are (5, -2).
Now, let's move on to the 180-degree rotation. To rotate a point (x, y) 180 degrees counterclockwise, we can use the formulas:
x' = -x
y' = -y
Applying these formulas to each vertex of the original triangle, we get:
For vertex R(-1, 3):
x' = 1
y' = -3
So, the coordinates of R'' are (1, -3).
For vertex S(4, -2):
x' = -4
y' = 2
So, the coordinates of S'' are (-4, 2).
For vertex T(2, -5):
x' = -2
y' = 5
So, the coordinates of T'' are (-2, 5).
Finally, let's move on to the 270-degree rotation. To rotate a point (x, y) 270 degrees counterclockwise, we can use the formulas:
x' = y
y' = -x
Applying these formulas to each vertex of the original triangle, we get:
For vertex R(-1, 3):
x' = 3
y' = 1
So, the coordinates of R''' are (3, 1).
For vertex S(4, -2):
x' = -2
y' = -4
So, the coordinates of S''' are (-2, -4).
For vertex T(2, -5):
x' = -5
y' = 2
So, the coordinates of T''' are (-5, 2).
Now, you can plot the points R', S', T', R'', S'', T'', R''', S''', T''' to get the image triangle R'S'T'.