anthonysutton82

anthonysutton82

08.09.2021 •

Mathematics

Find the distance between the points in a coordinate plane. Write your answer as a decimal. $\left(-4,7.8\right),\left(-4,-3.5\right)$

The distance between the points is
.

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Ответ:

lordcaos066

10.11.2021

Option A -37.2°

Step-by-step explanation:

Given : Δ XYZ has vertices X(x_1,y_1)=(-1,-1) , Y(x_2,y_2)=(-2,1) and Z(x_3,y_3)=(1,2)

To find: Measure of angle Z (let $\theta$ )

Solution :

Since we know the vertices we find the slope of line by

Slope formula : $m=\frac{y_2-y_1}{x_2-x_1}$

Let m_1 be the slope between X and Z

$m_1=\frac{y_3-y_1}{x_3-x_1}$

$m_1=\frac{2-(-1)}{1-(-1)}$

$m_1=\frac{3}{2}$

Now, let m_2 be the slope between Y and Z

$m_2=\frac{y_3-y_2}{x_3-x_2}$

$m_2=\frac{2-1}{1-(-2)}$

$m_2=\frac{1}{3}$

Now, to find angle we apply angle-slope formula

Angle-slope formula → $tan\theta=\begin{vmatrix} \frac{m_1-m_2}{1+m_1m_2} \end{vmatrix}$

Putting values of slopes in the formula,

$tan\theta=\begin{vmatrix} \frac{\frac{3}{2}-\frac{1}{3}}{1+\frac{3}{2}\times\frac{1}{3}} \end{vmatrix}$

$tan\theta=\begin{vmatrix} \frac{\frac{7}{6}}{1+\frac{1}{2}} \end{vmatrix}$

$tan\theta=\begin{vmatrix} \frac{\frac{7}{6}}{\frac{3}{2}} \end{vmatrix}$

$tan\theta=\begin{vmatrix} \frac{7\times 2}{6\times 3} \end{vmatrix}$

$tan\theta=\begin{vmatrix} \frac{7}{9} \end{vmatrix}$

$tan\theta=\frac{7}{9}$

$\theta=tan^{-1}\frac{7}{9}$

$\theta=37.2^{\circ}$

Refer the attached graph

Therefore, ∠Z= 37.2° option A

Triangle xyz has vertices x(–1, –1), y(–2, 1), and z(1, 2). what is the approximate measure of angle

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