QuestionJuly 18, 2025

For the points P and Q, find the distance d(P,Q) P(6sqrt (2),-4sqrt (11)),Q(8sqrt (2),9sqrt (11))

For the points P and Q, find the distance d(P,Q) P(6sqrt (2),-4sqrt (11)),Q(8sqrt (2),9sqrt (11))
For the points P and Q, find the distance d(P,Q) P(6sqrt (2),-4sqrt (11)),Q(8sqrt (2),9sqrt (11))

Solution
4.7(327 votes)

Answer

\sqrt{1867} Explanation 1. Identify the coordinates P(x_1, y_1) = (6\sqrt{2}, -4\sqrt{11}), Q(x_2, y_2) = (8\sqrt{2}, 9\sqrt{11}). 2. Apply the distance formula Use **d(P, Q) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}**. 3. Calculate differences x_2 - x_1 = 8\sqrt{2} - 6\sqrt{2} = 2\sqrt{2}; y_2 - y_1 = 9\sqrt{11} - (-4\sqrt{11}) = 13\sqrt{11}. 4. Square the differences (2\sqrt{2})^2 = 8; (13\sqrt{11})^2 = 1859. 5. Sum and take square root d(P, Q) = \sqrt{8 + 1859} = \sqrt{1867}.

Explanation

1. Identify the coordinates<br /> $P(x_1, y_1) = (6\sqrt{2}, -4\sqrt{11})$, $Q(x_2, y_2) = (8\sqrt{2}, 9\sqrt{11})$.<br />2. Apply the distance formula<br /> Use **$d(P, Q) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$**.<br />3. Calculate differences<br /> $x_2 - x_1 = 8\sqrt{2} - 6\sqrt{2} = 2\sqrt{2}$; $y_2 - y_1 = 9\sqrt{11} - (-4\sqrt{11}) = 13\sqrt{11}$.<br />4. Square the differences<br /> $(2\sqrt{2})^2 = 8$; $(13\sqrt{11})^2 = 1859$.<br />5. Sum and take square root<br /> $d(P, Q) = \sqrt{8 + 1859} = \sqrt{1867}$.
Click to rate:

Similar Questions