Answer:
C. sqrt((-3-6)² + (4+2)²)
Step-by-step 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
