Question

1. (20 points) let p = (-3,1) and q = (3,1) be points in the coordinate plane. (a) (5 points) find the distance between p and q.

Explanation:

Step1: Identify coordinates

Points \( P = (-3, 1) \) and \( Q = (3, 1) \). The y - coordinates are the same (\( y_1 = y_2 = 1 \)), so it's a horizontal line segment.

Step2: Use distance formula (or horizontal distance)

For horizontal points, distance \( d=\vert x_2 - x_1\vert \). Here, \( x_1=-3 \), \( x_2 = 3 \). So \( d=\vert3-(-3)\vert=\vert3 + 3\vert=\vert6\vert = 6 \).

Answer:

6