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Math  /  Geometry

QuestionDistance and Mldpoint
Find the distance between (0,0)(0,0) and (−5,−4)(-5,-4). V21 38\sqrt{ } 38 V17 V41

Studdy Solution

STEP 1

1. We are using the Cartesian coordinate system.
2. The distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is calculated using the distance formula.

STEP 2

1. Identify the coordinates of the two points.
2. Apply the distance formula.
3. Simplify the expression to find the distance.

STEP 3

Identify the coordinates of the two points. The first point is (0,0)(0, 0) and the second point is (−5,−4)(-5, -4).

STEP 4

Apply the distance formula, which is:
d=(x2−x1)2+(y2−y1)2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Substitute the given points (x1,y1)=(0,0)(x_1, y_1) = (0, 0) and (x2,y2)=(−5,−4)(x_2, y_2) = (-5, -4).
d=((−5)−0)2+((−4)−0)2 d = \sqrt{((-5) - 0)^2 + ((-4) - 0)^2}

STEP 5

Calculate the differences:
(−5)−0=−5 (-5) - 0 = -5 (−4)−0=−4 (-4) - 0 = -4
Substitute these values back into the formula:
d=(−5)2+(−4)2 d = \sqrt{(-5)^2 + (-4)^2}

STEP 6

Calculate the squares:
(−5)2=25 (-5)^2 = 25 (−4)2=16 (-4)^2 = 16
Substitute these values back into the formula:
d=25+16 d = \sqrt{25 + 16}

STEP 7

Add the squares:
25+16=41 25 + 16 = 41
Substitute this value back into the formula:
d=41 d = \sqrt{41}
The distance between the points (0,0)(0, 0) and (−5,−4)(-5, -4) is:
41 \boxed{\sqrt{41}}

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