Math

QuestionCalculate the distance between points G(5,4)G(-5,4) and H(2,6)H(2,6) in simplest exact form.

Studdy Solution

STEP 1

Assumptions1. The coordinates of point G are (-5,4) . The coordinates of point H are (,6)
3. We are asked to find the distance between these two points in the Cartesian coordinate system

STEP 2

We will use the distance formula to find the distance between two points in a Cartesian coordinate system. The distance formula is derived from the Pythagorean theorem and is given byd=(x2x1)2+(y2y1)2d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}where (x1,y1)(x1, y1) and (x2,y2)(x2, y2) are the coordinates of the two points.

STEP 3

Now, plug in the given values for the coordinates of points G and H into the distance formula.
d=(2(5))2+(6)2d = \sqrt{(2 - (-5))^2 + (6 -)^2}

STEP 4

implify the expressions inside the square root.
d=(2+)2+(64)2d = \sqrt{(2 +)^2 + (6 -4)^2}

STEP 5

Do the arithmetic inside the parentheses.
d=72+22d = \sqrt{7^2 +2^2}

STEP 6

Square the numbers inside the square root.
d=49+4d = \sqrt{49 +4}

STEP 7

Add the numbers inside the square root.
d=53d = \sqrt{53}So, the distance between points G and H is 53\sqrt{53} units.

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