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Math  /  Geometry

Question4 Fill in the Blank 1 point
Use the coordinate grid to find the exact distance between (−1,3)(-1,3) and (6,−6)(6,-6). Write the answer as a radical.
The exact distance between the points is the square root of □\square type your answer...

Studdy Solution

STEP 1

1. The distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) in a coordinate plane can be found using the distance formula.
2. The distance formula is derived from the Pythagorean theorem.

STEP 2

1. Identify the coordinates.
2. Apply the distance formula.
3. Simplify the expression under the square root.

STEP 3

Identify the coordinates of the two points. The first point is (−1,3)(-1, 3) and the second point is (6,−6)(6, -6).

STEP 4

Recall 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 points into the formula:
d=(6−(−1))2+(−6−3)2 d = \sqrt{(6 - (-1))^2 + (-6 - 3)^2}

STEP 5

Calculate the differences in the coordinates:
x2−x1=6−(−1)=6+1=7 x_2 - x_1 = 6 - (-1) = 6 + 1 = 7 y2−y1=−6−3=−9 y_2 - y_1 = -6 - 3 = -9
Substitute these values back into the formula:
d=72+(−9)2 d = \sqrt{7^2 + (-9)^2}

STEP 6

Calculate the squares of the differences:
72=49 7^2 = 49 (−9)2=81 (-9)^2 = 81
Add these squares together:
49+81=130 49 + 81 = 130

STEP 7

The exact distance between the points is the square root of the sum:
d=130 d = \sqrt{130}
The exact distance between the points is the square root of 130\boxed{130}.

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