The vertices of triangle ABC are A(-1 3) B(2 0) and C(0 6) .Transform the triangle ABC by the matrix formed by the extreme vertices of a unit square in order.Is the image of the triangle ABC a straight line? Write with reason.

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28-12-2023
Mathematics

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The vertices of triangle ABC are A(-1 3) B(2 0) and C(0 6) .Transform the triangle ABC by the matrix formed by the extreme vertices of a unit square in order.Is the image of the triangle ABC a straight line? Write with reason.

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aayoushpokhrel396 aayoushpokhrel396 · Answer 1 · 2023-12-28T16:27:01+01:00

Answer:

The extreme vertices of a unit square are typically (0,0), (1,0), (0,1), and (1,1).

The transformation matrix is formed by the extreme vertices of the unit square, so:

\[ \text{Transformation Matrix} = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix} \]

To transform the triangle ABC, each vertex of the triangle needs to be multiplied by this matrix:

A(-1, 3) becomes (0, 3, 2)

B(2, 0) becomes (0, 2, 1)

C(0, 6) becomes (6, 0, 5)

The transformed vertices are (0, 3, 2), (0, 2, 1), and (6, 0, 5). Connecting these points forms a plane rather than a straight line. Therefore, the image of triangle ABC after the transformation is not a straight line; it forms a plane in three-dimensional space.

The vertices of triangle ABC are A(-1 3) B(2 0) and C(0 6) .Transform the triangle ABC by the matrix formed by the extreme vertices of a unit square in order.Is the image of the triangle ABC a straight line? Write with reason.​

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The vertices of triangle ABC are A(-1 3) B(2 0) and C(0 6) .Transform the triangle ABC by the matrix formed by the extreme vertices of a unit square in order.Is the image of the triangle ABC a straight line? Write with reason.