Question

rotate a triangle defined by A(0,0),B(6,0)&(3,3) by 90° about origin in anticlockwise direction

Answer 1

Answer:

To rotate a triangle defined by the points A(0,0), B(6,0) and C(3,3) by 90° about the origin in the anticlockwise direction, we can use the matrix rotation method.

The matrix rotation method involves creating a transformation matrix that represents the rotation and then multiplying the matrix by the coordinates of the triangle's vertices.

Explanation:

Here is the rotation matrix for 90° anticlockwise rotation about the origin:

| cos(90)  -sin(90) |

| sin(90)   cos(90) |

The cos(90) = 0, sin(90) = 1

Then we will multiply the matrix with the coordinates of the three vertices of the triangle:

A(0,0) = | 0  0 | * | 0 |   = | 0 |

        | 0  0 |   | 0 |     | 0 |

B(6,0) = | 0 -6 | * | 6 |   = | 0 |

        | 6  0 |   | 0 |     |-6 |

C(3,3) = |-3  3 | * | 3 |   = |-3 |

        | 3  3 |   | 3 |     | 3 |

So after the rotation, the coordinates of the triangle's vertices will be:

A(0,0)

B(0,-6)

C(-3,3)

The triangle is rotated 90° about the origin in the anticlockwise direction.

It is worth noting that, this method can be applied for any degree of rotation about the origin and for any shape.

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