Question

What is the distance between (-2 1/2, -3) and (1, -3)​

Answer 1

The distance between (-2 1/2, -3) and (1, -3)​ will be:

• 
  `d=(7)/(2)`

Explanation:

Given the points

• (-2 1/2, -3)

• (1, -3)​

`\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a(b)/(c)=(a\cdot \:c+b)/(c)`

`-2(1)/(2)=-(5)/(2)`

so the point becomes (-5/2, -3)

Finding the distance between (-5/2, -3) and (1, -3):

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

`\mathrm{The\:distance\:between\:}\left(-(5)/(2),\:-3\right)\mathrm{\:and\:}\left(1,\:-3\right)\mathrm{\:is\:}`

`d=\sqrt{\left(1-\left(-(5)/(2)\right)\right)^2+\left(-3-\left(-3\right)\right)^2}`

`=\sqrt{\left((5)/(2)+1\right)^2+\left(3-3\right)^2}`

`=\sqrt{(7^2)/(2^2)+0}`

`=\sqrt{(7^2)/(2^2)}`

`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{(a)/(b)}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0`

`=(√(7^2))/(√(2^2))`

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

`=(7)/(2)`

Thus, the distance between (-2 1/2, -3) and (1, -3)​ will be:

• 
  `d=(7)/(2)`