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Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin?

(4, 2)
(2, 4)
(–4, –2)
(–2, –4)

3 answers

To find the coordinates of point B after a 270° rotation about the origin, we can use the rotation transformation rules.

The general rule for rotating a point \((x, y)\) counterclockwise by 270° (which is the same as a clockwise rotation of 90°) about the origin is given by: \[ (x, y) \rightarrow (y, -x) \]

If we denote the original point \(B\) as \((x, y)\), after applying the transformation for a 270° rotation:

  1. Let \(B\) be at coordinates \((x, y)\).
  2. After the rotation, the new coordinates will be \((y, -x)\).

Now, without knowing the exact coordinates of point B, we cannot calculate the result directly. However, let's consider each of the answer choices provided and see how to reach them:

  1. If \(B = (4, 2)\):
    • After rotation: \((2, -4)\)
  2. If \(B = (2, 4)\):
    • After rotation: \((4, -2)\)
  3. If \(B = (-4, -2)\):
    • After rotation: \((-2, 4)\)
  4. If \(B = (-2, -4)\):
    • After rotation: \((-4, 2)\)

Among the options provided:

  • \((4, 2)\) rotates to \((2, -4)\)
  • \((2, 4)\) rotates to \((4, -2)\)
  • \((-4, -2)\) rotates to \((-2, 4)\)
  • \((-2, -4)\) rotates to \((-4, 2)\)

It's important to determine the starting coordinates of point B. If you check the coordinates of B directly from your graph, you can apply the rotations above accordingly.

Please provide the coordinates of point B, and I can give the exact answer based on the rotation.

Point B is (-2,4)

Given that the coordinates of point B are \((-2, 4)\), we will apply the 270° rotation transformation about the origin.

Using the transformation rule for a 270° rotation, which is: \[ (x, y) \rightarrow (y, -x) \]

we substitute the coordinates of point B:

  • \(x = -2\)
  • \(y = 4\)

Now applying the transformation: \[ (-2, 4) \rightarrow (4, -(-2)) \rightarrow (4, 2) \]

After the rotation, the coordinates of point B will be \((4, 2)\).

Thus, the coordinates of the image of point B after the triangle is rotated 270° about the origin are \(\boxed{(4, 2)}\).