Question

A grid shows the position of a subway stop and your house. The subway stop is located at (-6,3) and your house is located at (6,1) what is the distance to the nearest unit, between your house and the subway stop?

Answer 1

use the length of a line equation d= The square root of (x2-x1)^2+(y2-y1)^2

Answer 2

plug in the coordinates (6-(-6))^2 + (1-3)^2
=(12)^2+(4)^2
=144+16
=160 "now square 160"
= about 12.6 units away

Answer 3

If you plot these two points on a coordinate plane, you'll see that you can connect them using a diagonal line. You'll also see that if you draw a horizontal line with an x coordinate of 1 and vertical line with a y coordinate of -6, you'll have created a right triangle that goes through both of these points.
Using the coordinate plane, you know the lengths of two sides of this right triangle, and need to determine the length of the hypotenuse. This now becomes a simple Pythagorean Theorem problem : \[a^{2} + b ^{2} = c ^{2}\]

Let's call the long horizontal line A - this is the horizontal distances between 6 and -6, or 12 units.

The vertical line will be B - the distance between 1 and 3, or 2 units.

Now we can solve using the formula above,

12^2 + 2^2 = c^2\[12^{2} + 2^{2} = c ^{2}\]

\[\sqrt{144 + 4}\] = \[\sqrt{148}\]

The square root of 148 is 12.166, which when rounded to the closest whole unit is 12.

Therefore, the length of the diagonal line running from the subway station to your house is approximately 12 units long.

Answer 4

Thanks my instructor explained as creating a right triangle with the equation and plugin them in into the a quadratic equation 00 but this is way better of an explination.