Answer the questions by drawing on the coordinate plane below.

(a) draw the image of ∆jkl after a rotation of 90°clockwise about the origin. label the image ∆j’k’l’.

(b) draw the image of ∆jkl under the dilation with scale factor ½ and center of dilation at the origin.

label the image ∆j”k”l”.

Answer the questions by drawing on the coordinate plane below. (a) draw the image of ∆jk

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Ответ:

smithsa10630

15.05.2022

Mathematics

The length of BC is $4 \sqrt{5}$ .

Solution:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 16 and DC = 5

Leg rule of geometric mean theorem:

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$

$\Rightarrow \frac{AC}{BC}=\frac{BC}{DC}$

$\Rightarrow \frac{16}{x}=\frac{x}{5}$

Do cross multiplication.

$\Rightarrow 16\times 5 = x\times x$

$\Rightarrow 80= x^2$

$\Rightarrow 16\times 5= x^2$

Taking square root on both sides.

$\Rightarrow \sqrt{16\times 5} = \sqrt{x^2}$

$\Rightarrow \sqrt{4^2\times 5} = \sqrt{x^2}$

square and square roots get canceled, we get

$\Rightarrow 4\sqrt{ 5} = x$

The length of BC is $4 \sqrt{5}$ .

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