Question

What is the distance between the origin and (−3,−4)? A. 5 B. 7 C. 12 D. 25

Answer 1

The distance between the origin and (-3,-4) can be modeled with a triangle. The horizontal distance and vertical distance are two legs, and the distance between the origin and the point is the hypotenuse.

Since we are dealing with distance, we will use absolute values for the distances.

The origin is at (0,0), and the point is at (-3,-4). Add the x-values and y-values:

$|0 + -3| = |-3| = 3$

$|0 + -4| = |-4| = 4$

The two legs of the triangles are 3 and 4.

We'll use the Pythagorean theorem to find the distance. Square the two legs' lengths:

$(3^2 + 4^2) = x^2 = (9 + 16) = 25 = x^2$

Square root both sides to get x by itself:

$\boxed{x = 5}$

The distance between the origin and (-3,-4) will be 5.

Answer 2

To find the answer to this question you create a traingle using the origin and the plot given. Then when that is completed you count up which is  a. 5