How do you find the distance between (- 9,- 9)(−9,−9) and ( - 54,191)(−54,191)?

1 Answer
smendyka
Oct 1, 2017

See a solution process below:

Explanation:

The formula for calculating the distance between two points is:

d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)d=√(x2−x1)2+(y2−y1)2

Substituting the values from the points in the problem gives:

d = sqrt((color(red)(-54) - color(blue)(-9))^2 + (color(red)(191) - color(blue)(-9))^2)d=√(−54−−9)2+(191−−9)2

d = sqrt((color(red)(-54) + color(blue)(9))^2 + (color(red)(191) + color(blue)(9))^2)d=√(−54+9)2+(191+9)2

d = sqrt((-45)^2 + 20^2)d=√(−45)2+202

d = sqrt(2025 + 400)d=√2025+400

d = sqrt(2425)d=√2425

d = sqrt(25 * 97)d=√25⋅97

d = sqrt(25)sqrt(97)d=√25√97

d = 5sqrt(97)d=5√97

If a single number is needed:

d = 49.244d=49.244 rounded to the nearest thousandth

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