Question

1. graph the two points on the coordinate grid. then find the length of the segment that connects them.

a. ( a(-4, 4) ), ( b(2, 4) )
b. ( p(-4, 4) ), ( q(2, -4) )

Explanation:

Part a

Step1: Analyze coordinates

Points \( A(-4, 4) \) and \( B(2, 4) \) have the same \( y \)-coordinate, so the segment is horizontal.

Step2: Calculate length

For horizontal segments, length is \( |x_2 - x_1| \). Here, \( x_1 = -4 \), \( x_2 = 2 \). So length \( = |2 - (-4)| = |6| = 6 \).

Step1: Use distance formula

The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). For \( P(-4, 4) \) and \( Q(2, -4) \), \( x_1 = -4 \), \( y_1 = 4 \), \( x_2 = 2 \), \( y_2 = -4 \).

Step2: Substitute values

\( d = \sqrt{(2 - (-4))^2 + (-4 - 4)^2} = \sqrt{(6)^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \).

Answer:

6

Part b