Calculate the distance between the points =G−8, 5 and =Q−1, 2 in the coordinate plane.Give an exact answer (not a decimal approximation).

To calculate the distance between two points in a coordinate plane, we use the distance formula which is derived from the Pythagorean theorem. The distance d between two points with coordinates (x1, y1) and (x2, y2) is given by:

d = sqrt[(x2 - x1)² + (y2 - y1)²]

Here, the coordinates for point G are (-8, 5) and for point Q are (-1, 2).

So, x1 = -8, y1 = 5, x2 = -1, and y2 = 2.

Substitute these values into the distance formula:

d = sqrt[(-1 - (-8))² + (2 - 5)²] d = sqrt[(7)² + (-3)²] d = sqrt[(49) + (9)] d = sqrt[58]

So, the distance between points G and Q is sqrt[58] units.