Question

Which expression gives the distance between the points

(-3, 4) and (6,-2)?
O A. (-3 - 4) * +(6+2)
O B. (-3-6)* + (4 +2)
O c. +(-3-6)* +(4+2) ?
O D. (-3 - 4) * +(6+2)

Answer 1

C. sqrt((-3-6)² + (4+2)²)

Explanation:

as we are using Pythagoras and asking for the distance as a side length (actually the Hypotenuse, the side opposite of the 90 degree angle) in a right-angled triangle, only an expression of a square root of a sum of squares can be right.

so, A and B are automatically out without even further analysis.

for the distance between 2 points on a coordination grid we build the mentioned right-angled triangle with the difference in x-direction as one side (e.g. "a"), the difference in y-direction as a second side (e.g. "b").

and the direct distance is then the Hypotenuse "c".

you remember Pythagoras :

c² = a² + b²

and therefore

c = sqrt(a² + b²)

in our example "a" is the difference between the 2 x-values.

a = (-3 - 6)

and "b" is the difference between the 2 y-values.

b = (4 - -2) = (4 + 2)

since we have to square them for the formula, the direction of what is subtracted from what is irrelevant, as the square of a negative value is also positive.

c = sqrt((-3 - 6)² + (4 + 2)²)

and that is answer option C