Question

Find the distance when y2=9, y1=13, x2=4, and x1=0.

Answer 1

Answer:

Tthe distance between $\left(x_1,\:y_1\right)=\left(0,\:13\right)$ and $\left(x_2,\:y_2\right)=\left(4,\:9\right)$ will be:

• $\mathrm{Distance\:between\:}\left(0,\:13\right)\mathrm{\:and\:}\left(4,\:9\right):\quad 4\sqrt{2}$

Step-by-step explanation:

Given the points

• $\left(x_1,\:y_1\right)=\left(0,\:13\right)$

• $\left(x_2,\:y_2\right)=\left(4,\:9\right)$

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$\mathrm{The\:distance\:between\:}\left(0,\:13\right)\mathrm{\:and\:}\left(4,\:9\right)\mathrm{\:is\:}$

$=\sqrt{\left(4-0\right)^2+\left(9-13\right)^2}$

$=\sqrt{4^2+4^2}$

$=\sqrt{4^2\cdot \:2}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0$

$=\sqrt{2}\sqrt{4^2}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

$=4\sqrt{2}$

Therefore, the distance between $\left(x_1,\:y_1\right)=\left(0,\:13\right)$ and $\left(x_2,\:y_2\right)=\left(4,\:9\right)$ will be:

• $\mathrm{Distance\:between\:}\left(0,\:13\right)\mathrm{\:and\:}\left(4,\:9\right):\quad 4\sqrt{2}$