Question

1. what is the distance between the points h(-5,9) and j(1,6)?

8.2
16.1
14.9
6.7

Explanation:

Step1: Recall Distance Formula

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

Step2: Identify Coordinates

For points \( H(-5, 9) \) and \( J(1, 6) \), \( x_1 = -5 \), \( y_1 = 9 \), \( x_2 = 1 \), \( y_2 = 6 \).

Step3: Calculate Differences

\( x_2 - x_1 = 1 - (-5) = 6 \), \( y_2 - y_1 = 6 - 9 = -3 \).

Step4: Square Differences

\( (x_2 - x_1)^2 = 6^2 = 36 \), \( (y_2 - y_1)^2 = (-3)^2 = 9 \).

Step5: Sum and Square Root

Sum: \( 36 + 9 = 45 \), Distance: \( \sqrt{45} \approx 6.7 \).

Answer:

6.7 (corresponding to the option with 6.7)