Question

given: p(-5, -4), q(7, -8) find: pq

Explanation:

Step1: Recall distance formula

The distance between two points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Here, \( x_1 = -5 \), \( y_1 = -4 \), \( x_2 = 7 \), \( y_2 = -8 \).

Step2: Substitute values into formula

Calculate \( x_2 - x_1 = 7 - (-5) = 12 \), \( y_2 - y_1 = -8 - (-4) = -4 \).
Then, \( (x_2 - x_1)^2 = 12^2 = 144 \), \( (y_2 - y_1)^2 = (-4)^2 = 16 \).

Step3: Sum and take square root

Sum: \( 144 + 16 = 160 \).
Distance \( PQ = \sqrt{160} = \sqrt{16 \times 10} = 4\sqrt{10} \).

Answer:

\( 4\sqrt{10} \)