Question

We want to determine which point is closer to the origin: M (-1, -6) or N (-8, 10). Find the distance.

A. M is closer
B. N is closer
C. Both are equidistant
D. Cannot determine

Answer 1

To determine which point is closer to the origin, we can calculate the distance between each point and the origin using the distance formula. Point M (-1, -6) is closer to the origin.

Step-by-step explanation:

To determine which point is closer to the origin, we can calculate the distance between each point and the origin using the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For point M(-1, -6) with coordinates (x1, y1) = (-1, -6) and the origin with coordinates (x2, y2) = (0, 0), the distance is:

d1 = sqrt((-1 - 0)^2 + (-6 - 0)^2) = sqrt(1 + 36) = sqrt(37)

For point N(-8, 10) with coordinates (x1, y1) = (-8, 10), the distance is:

d2 = sqrt((-8 - 0)^2 + (10 - 0)^2) = sqrt(64 + 100) = sqrt(164)

Since sqrt(164) is greater than sqrt(37), point M is closer to the origin. Therefore, the answer is A. M is closer.