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Math  /  Geometry

QuestionFind the distance between the points ( -9 , 7) and (9,20)(9,20). 493\sqrt{493} 493 155\sqrt{155} 155

Studdy Solution

STEP 1

1. We are given two points in a two-dimensional Cartesian coordinate system: (−9,7)(-9, 7) and (9,20)(9, 20).
2. The distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) in a Cartesian plane can be found using the distance formula: d=(x2−x1)2+(y2−y1)2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

STEP 2

1. Identify the coordinates of the given points.
2. Apply the distance formula to the given points.
3. Simplify the expression under the square root.
4. Compute the final distance.

STEP 3

Identify the coordinates of the given points: (x1,y1)=(−9,7) (x_1, y_1) = (-9, 7) (x2,y2)=(9,20) (x_2, y_2) = (9, 20)

STEP 4

Apply the distance formula: d=(x2−x1)2+(y2−y1)2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Substitute the given coordinates: d=(9−(−9))2+(20−7)2 d = \sqrt{(9 - (-9))^2 + (20 - 7)^2}

STEP 5

Simplify the expressions inside the parentheses: d=(9+9)2+(20−7)2 d = \sqrt{(9 + 9)^2 + (20 - 7)^2} d=182+132 d = \sqrt{18^2 + 13^2}

STEP 6

Compute the squares: d=324+169 d = \sqrt{324 + 169}

STEP 7

Add the values under the square root: d=493 d = \sqrt{493}

STEP 8

The final distance between the points (−9,7)(-9, 7) and (9,20)(9, 20) is: d=493 d = \sqrt{493}
Solution: The distance between the points is 493\sqrt{493}.

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