For the points P and Q, find the distance d(P, Q).
-$$\mathrm { P } ( 9 \sqrt { 11 } , - 2 \sqrt { 7 } ) , \mathrm { Q } ( - 3 \sqrt { 11 } , - 7 \sqrt { 7 } )$$
A) $\sqrt { 1759 }$
B) 1759
C) $\sqrt { 167 }$
D) 167

Question

Quizplus · Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Applying this formula to points P and Q, we get $\sqrt{[(9\sqrt{11} - (-3\sqrt{11}))^2 + (-2\sqrt{7} - (-7\sqrt{7}))^2]}$ = $\sqrt{(12\sqrt{11})^2 + (5\sqrt{7})^2}$ = $\sqrt{144 \cdot 11 + 25 \cdot 7}$ = $\sqrt{1584 + 175}$ = $\sqrt{1759}$.

For the Points P and Q, Find the Distance D(P P(911,−27),Q(−311,−77)\mathrm { P } ( 9 \sqrt { 11 } , - 2 \sqrt { 7 } ) , \mathrm { Q } ( - 3 \sqrt { 11 } , - 7 \sqrt { 7 } )P(911​,−27​),Q(−311​,−77​)

For the Points P and Q, Find the Distance D(P $\mathrm { P } ( 9 \sqrt { 11 } , - 2 \sqrt { 7 } ) , \mathrm { Q } ( - 3 \sqrt { 11 } , - 7 \sqrt { 7 } )$