The coordinates of point P P P are (6,−7) (6, -7) (6,−7), and the coordinates of point Q Q Q are (2,−5) (2, -5) (2,−5).
The distance d(P,Q) d(P, Q) d(P,Q) between two points P(x1,y1) P(x_1, y_1) P(x1,y1) and Q(x2,y2) Q(x_2, y_2) Q(x2,y2) is given by: d(P,Q)=(x2−x1)2+(y2−y1)2 d(P, Q) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} d(P,Q)=(x2−x1)2+(y2−y1)2
Substitute x1=6 x_1 = 6 x1=6, y1=−7 y_1 = -7 y1=−7, x2=2 x_2 = 2 x2=2, and y2=−5 y_2 = -5 y2=−5 into the formula: d(P,Q)=(2−6)2+(−5−(−7))2 d(P, Q) = \sqrt{(2 - 6)^2 + (-5 - (-7))^2} d(P,Q)=(2−6)2+(−5−(−7))2
Calculate the differences: 2−6=−4and−5−(−7)=2 2 - 6 = -4 \quad \text{and} \quad -5 - (-7) = 2 2−6=−4and−5−(−7)=2 Now, square these differences: (−4)2=16and22=4 (-4)^2 = 16 \quad \text{and} \quad 2^2 = 4 (−4)2=16and22=4
Add the squared differences: 16+4=20 16 + 4 = 20 16+4=20 Take the square root of 20: 20=25 \sqrt{20} = 2\sqrt{5} 20=25
The distance d(P,Q) d(P, Q) d(P,Q) is 25 \boxed{2\sqrt{5}} 25.
Oops, Image-based questions are not yet availableUse Solvely.ai for full features.
Failed. You've reached the daily limit for free usage.Please come back tomorrow or visit Solvely.ai for additional homework help.