Math

QuestionFind the distance between points (1,2)(-1,2) and (3,4)(3,4). Options: a) 5 b) 8\sqrt{8} c) 10\sqrt{10} d) 20\sqrt{20} e) 40\sqrt{40}.

Studdy Solution

STEP 1

Assumptions1. The coordinates of the first point are (-1,) . The coordinates of the second point are (3,4)
3. We are asked to find the Euclidean distance between these two points

STEP 2

The Euclidean distance between two points (x1,y1)(x1, y1) and (x2,y2)(x2, y2) in a plane is given by the formulaDistance=(x2x1)2+(y2y1)2Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}

STEP 3

Now, plug in the given values for the coordinates of the two points into the formula.
Distance=(3(1))2+(2)2Distance = \sqrt{(3 - (-1))^2 + ( -2)^2}

STEP 4

implify the expressions inside the square root.
Distance=(3+1)2+(42)2Distance = \sqrt{(3 +1)^2 + (4 -2)^2}

STEP 5

Calculate the squares.
Distance=42+22Distance = \sqrt{4^2 +2^2}

STEP 6

Calculate the square of the numbers.
Distance=16+4Distance = \sqrt{16 +4}

STEP 7

Add the numbers inside the square root.
Distance=20Distance = \sqrt{20}So, the distance between points (-1,2) and (3,4) is 20\sqrt{20}.

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