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Calculate the distance between the points G=(0,7) and L=(-8,2) in the coordinate plane. Round your answer to the nearest hundredth.

Calculate the distance between the points G=(0,7) G=(0,7) and L=(−8,2) L=(-8,2) in the coordinate plane. Round your answer to the nearest hundredth.

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Full solution

Q. Calculate the distance between the points G=(0,7) G=(0,7) and L=(−8,2) L=(-8,2) in the coordinate plane. Round your answer to the nearest hundredth.
  1. Use Distance Formula: To find the distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), use the distance formula: d=((x2−x1)2+(y2−y1)2)d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}.
  2. Plug in Coordinates: Plug in the coordinates of G=(0,7)G=(0,7) and L=(−8,2)L=(-8,2) into the distance formula: d=((−8−0)2+(2−7)2)d = \sqrt{((-8 - 0)^2 + (2 - 7)^2)}.
  3. Calculate Squares: Calculate the squares: d=((−8)2+(−5)2)=64+25d = \sqrt{((-8)^2 + (-5)^2)} = \sqrt{64 + 25}.
  4. Add Squares: Add the squares: d=64+25=89d = \sqrt{64 + 25} = \sqrt{89}.
  5. Find Square Root: Use a calculator to find the square root of 8989: d≈89≈9.433981132056603d \approx \sqrt{89} \approx 9.433981132056603.
  6. Round to Nearest Hundredth: Round the result to the nearest hundredth: d≈9.43d \approx 9.43.

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