Question

Rotate a right triangle with points 2,3 4,7 5,4 90 degrees to the vertex point 2,3.

Answer 1

Is it 2,3 -2,5 1,6?

Answer 2

Your post: Rotate a right triangle with points 2,3 4,7 5,4 90 degrees to the vertex point 2,3.

rephrased:
Rotate a right triangle with points (2,3), (4,7), and (5,4) by 90° about the vertex point (2,3) counterclockwise .

Your answer is correct, I am curious what method you used.

Answer 3

(x,y)→(2-(y-3),3+(x-2)) = (5-y,1+x)

Answer 4

I put perpendicular lines through the vertex point and rotated it

Answer 5

[AI-generated answer — Explain Bot]

To rotate a right triangle 90 degrees counterclockwise around a given vertex, you can use the following steps:

1. Calculate the distance between each point and the vertex point (2,3).
2. Subtract the x-coordinate of the vertex point from each point's x-coordinate.
3. Subtract the y-coordinate of the vertex point from each point's y-coordinate.
4. Swap the new x and y coordinates, but negate the new x-coordinate.
5. Add the x-coordinate of the vertex point to the new x-coordinate.
6. Add the y-coordinate of the vertex point to the new y-coordinate.

Let's apply these steps to rotate the right triangle with points (2,3), (4,7), and (5,4) 90 degrees counterclockwise around the vertex point (2,3):

1. Calculate the distances:
- Point A: √((2 - 2)^2 + (3 - 3)^2) = 0
- Point B: √((4 - 2)^2 + (7 - 3)^2) = √(2^2 + 4^2) = √20
- Point C: √((5 - 2)^2 + (4 - 3)^2) = √(3^2 + 1^2) = √10

2. Subtract the x-coordinate of the vertex point from each point's x-coordinate:
- Point A: 2 - 2 = 0
- Point B: 4 - 2 = 2
- Point C: 5 - 2 = 3

3. Subtract the y-coordinate of the vertex point from each point's y-coordinate:
- Point A: 3 - 3 = 0
- Point B: 7 - 3 = 4
- Point C: 4 - 3 = 1

4. Swap the new x and y coordinates, but negate the new x-coordinate:
- Point A: (0, 0) remains the same
- Point B: (4, -2)
- Point C: (1, -3)

5. Add the x-coordinate of the vertex point to the new x-coordinate:
- Point A: (2 + 0, 3 + 0) = (2, 3) remains the same
- Point B: (2 + 4, 3 + (-2)) = (6, 1)
- Point C: (2 + 1, 3 + (-3)) = (3, 0)

6. Add the y-coordinate of the vertex point to the new y-coordinate:
- Point A: (2, 3) remains the same
- Point B: (6, 1 + 3) = (6, 4)
- Point C: (3, 0 + 3) = (3, 3)

So, the rotated right triangle will have the new points: (2,3), (6,4), and (3,3).