Question

Find the distance between the points (0, 2) and (-9, -10).

Answer 1

Answer: The distance is 15 units.

Explanation:

Find the difference in the x and y coordinates and square them and add them together.

(0,2) and (-9,-10) The x coordinates are 0 and -9 and the y coordinates are 2 and -10.

0-(-9) = 9

2-(-10) = 12

9^2 + 12^2 = d^2

81 + 144 = d^2

225 = d^2

d =
`√(225)`

d= 15

Answer 2

15

Explanation:

OPTION 1:

We can use the distance formula to find the distance between these two points.

`√((x_2-x_1)^2 + (y_2-y_1)^2)`

X2 is -9, X1 is 0, Y2 is -10, and Y1 is 2, so we can substitute inside the equation.

`√((-9-0)^2 + (-10-2)^2)\\\\√(9^2 + -12^2)\\\\√(81 + 144)\\\\√(225)\\\\15`

OPTION 2:

We can look at the change in x and the change in y and use the Pythagorean Theorem to find the missing length of the hypotenuse.

The x changes by 9, and the Y changes by 12.

`a^2+b^2=c^2` is the Pythagorean Theorem. We know a and b, so we can substitute inside the equation.

`9^2 + 12^2 = c^2\\\\81+144=c^2\\\\225=c^2\\\\c=15`

Hope this helped!