Question

Find the distance between (7 -4) (3 4)

Answer 1

Answer:

Let the points be P(7, -4) and Q(3, 4).

Then,

$PQ = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \: \: \: \: \: \\ = \sqrt{ {(3 - 7)}^{2} + {(4 - ( - 4))}^{2} } \\ = \sqrt{ {(3 - 7)}^{2} + {(4 + 4)}^{2}} \: \: \: \: \: \: \: \\ = \sqrt{ {( - 4)}^{2} + {(8)}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = \sqrt{16 + 64} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = \sqrt{80} = \sqrt{2 \times 2 \times 2 \times 5} \: \: \: \\ = 2 \sqrt{10} \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence, the distance between P and Q is 2√10 cm.