Math  /  Geometry

QuestionSaudy A(0,0),B(6,1),C(2,6)A^{\prime}(0,0), B^{\prime}(-6,-1), C^{\prime}(-2,-6) 0), B(6,1)B(6,1), and coordinates A(0A(0,
A triangle has 0),B(6,1)0), B(6,1), and C(2,6)C(2,6). Find the coordinates of A,BA^{\prime}, B^{\prime}, and CC^{\prime} A(0,0),B(6,1),C(2,6)A^{\prime}(0,0), B^{\prime}(6,-1), C^{\prime}(2,-6) after a 180180^{\circ} rotation around Point AA. A(0,0),B(6,1),C(2,6)A^{\prime}(0,0), B^{\prime}(-6,1), C^{\prime}(-2,6) Back Nexps

Studdy Solution

STEP 1

What is this asking? We need to find the new coordinates of a triangle after spinning it 180 degrees around one of its corners. Watch out! Rotating 180 degrees isn't the same as just flipping the signs!
Think about what happens when you turn something halfway around.

STEP 2

1. Set up the rotation
2. Rotate point B
3. Rotate point C

STEP 3

Alright, so we're rotating around point A, which has coordinates (0,0)(0, 0).
This is **super helpful** because it makes the math much easier!
When we rotate around the origin, the rule for a 180-degree rotation is (x,y)(x,y)(x, y) \rightarrow (-x, -y).
Basically, we just flip the signs of both the x and y coordinates.

STEP 4

Point B starts at (6,1)(6, 1).
Let's apply our rotation rule!
We flip the sign of the x-coordinate, +6+6 becomes 6-6.
We flip the sign of the y-coordinate, +1+1 becomes 1-1.
So, the new coordinates of B, which we'll call B', are (6,1)(-6, -1).
Boom!

STEP 5

Point C starts at (2,6)(2, 6).
Using the same rotation rule, we flip the signs.
The x-coordinate +2+2 becomes 2-2, and the y-coordinate +6+6 becomes 6-6.
So, C' is at (2,6)(-2, -6).
Fantastic!

STEP 6

After the rotation, the new coordinates are A' (0,0)(0, 0), B' (6,1)(-6, -1), and C' (2,6)(-2, -6).

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