Question

What is the approximate distance between the points (1,-2) and (-9,3) on a coordinate grid

Answer 1

`5√(5)` ≈ 11.1803398874989485

Detailed Explanation

We will be using the distance formula for this problem

`√(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

Now, let's input the numbers into the formula.

`√(\left(-9-1\right)^2+\left(3-\left(-2\right)\right)^2)`

Solve.

Therefore, the distance between the two points is

`5√(5)` ≈ 11.1803398874989485

Answer 2

11,18

Explanation:

If you put those points (1,-2) and (-9,3) on a coordinate grid

You get an triangle that has a right angle (90°) with sides:

-5 and 10 (a,b)

(x1,y1)=(1,-2)

(x2,y2)=(-9,3)

x1-x2=1-(-9)=10

y1-y2=-2-3=-5

Then you can use Pythagoras' Theorem to calculate c, which is the hypotenuse (the shortest distance between the two points):

Start with: a^2 + b^2 = c^2

Put in what we know: (-5^2)+(10^2)= c^2

Calculate squares: 25 + 100 = c^2

Swap sides: c^2 = 125

Square root of both sides: c = √125

Calculate: c = 11,18