Question

Use scalar multiplication to determine the coordinates of the vertices of the dilated figure.
Triangle with vertices A(1, 8), B(6, 1), and c(-9, 4) with scale factor 5/2

Answer 1

The coordinates of the vertices of the dilated figure are A'(1.25, 10), B'(7.5, 1.25), and C'(-11.25, 5).

Scalar Multiplication

The multiplication of a vector with a positive real number without changing its direction is called scalar multiplication.

How to find the vertices of the dilated figure?

The given triangle has the vertices A(1,8), B(6,1), and C(-9,4).

The matrix representation of the triangle ABC is,

$\left[\begin{array}{ccc}1&6&-9\\8&1&4\end{array}\right]$

And the scale factor is 5/2.

The matrix representation of the dilated figure can be obtained by multiplying the above matrix with 5/4.

$=\dfrac{5}{4}\left[\begin{array}{ccc}1&6&-9\\8&1&4\end{array}\right]$

$=\left[\begin{array}{ccc}\dfrac{5}{4}&\dfrac{15}{2}&\dfrac{-45}{4}\\10&\dfrac{5}{4}&5\end{array}\right]$

$=\left[\begin{array}{ccc}1.25&7.5&-11.25\\10&1.25&5\end{array}\right]$

Hence, the coordinates of the vertices of the dilated figure are A'(1.25, 10), B'(7.5, 1.25), and C'(-11.25, 5).

Learn more about dilated figures here - https://brainly.com/question/18068466

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