Question

What is the distance between the points whose coordinates are (-4, 3) and (9, 15)?​

Answer 1

$\large\underline{\mathbb{\blue{ \: \: \: DISTANCE \: \: \: }}}:$

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$\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\ \end{gathered}$

$\qquad \qquad\quad \large \boxed{ \bold{ \:\: \pmb{17.69 \:units \: \: }}}$

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${\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}$

Determine the length from point A to point B using the given formula.

$\begin{gathered}\begin{gathered}\bold{Formula : } \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \\ \boxed{\rm \: \: \: D= \sqrt{(x_2 - x_1 {)}^{2} + (y_2 - y_1 {)}^{2} } \: \: \: }\\\end{gathered} \end{gathered}$

$\begin{gathered} \qquad \qquad \quad \hookrightarrow \: \: \tt{(x_1, y_1) = \green{ (-4,3) }}\\\end{gathered}$

$\begin{gathered} \qquad \qquad \quad \hookrightarrow \: \: \tt{(x_2, y_2) = \blue{(9,15) }} \\ \end{gathered}$

Substitute in the two values of x and y coordinates.

$\sf \implies Distance = \sqrt{(\blue{9}\:- \: \green{-4}{)}^{2} + (\blue{15}\:-\:\green{3}{)}^{2} }$

$\begin{gathered} \sf: \implies Distance = {\pink{\sqrt{(13 {)}^{2}}} + \purple{(12{)}^{2}} }\\\end{gathered}$

$\begin{gathered} \sf: \implies Distance = {\red{\sqrt{(169) }}+ \blue{(144)}}\\\end{gathered}$

$\begin{gathered} \sf: \implies Distance = \pmb{\sqrt{313}}\\\end{gathered}$

$\begin{gathered} \sf: \implies Distance = \pmb{17.69}\\\end{gathered}$

Therefore, the distance between two points is 17.69 units or $\pmb{\sf{D=\sqrt{313}}}$.

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$\large \tt{08/18/2022 \quad \qquad- \sf\copyright \: \large\tt{Eutoroxia}}$

Answer 2

Answer:

$\sf distance=\sqrt{313}=17.7\:units\:\:(nearest\:tenth)$

Step-by-step explanation:

Distance between two points

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points.}$

Given points:

• $\textsf{Let }(x_1,y_1)=(-4,3)$

• $\textsf{Let }(x_2,y_2)=(9,15)$

Substitute the given points into the formula and solve for d:

$\begin{aligned}d & =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\implies d & =\sqrt{(9-(-4))^2+(15-3)^2}\\ & =\sqrt{13^2+12^2}\\ & =\sqrt{169+144}\\ & =\sqrt{313}\\ & =17.7\:\: \sf (nearest\:tenth)\end{aligned}$

Therefore, the distance between the points (-4, 3) and (9, 15) is $\sf \sqrt{313}$ units.

Learn more about the distance formula here:

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