Math

QuestionFind the distance between the points (3,1)(3,1) and (7,7)(7,7) using the distance formula.

Studdy Solution

STEP 1

Assumptions1. The given points are (3,1) and (7,7) . We are working in a-dimensional Cartesian coordinate system

STEP 2

The distance between two points (x1,y1)(x1, y1) and (x2,y2)(x2, y2) in a2-dimensional Cartesian coordinate system can be calculated using the distance formula, which is derived from the Pythagorean theorem. The formula is as followsDistance=(x2x1)2+(y2y1)2Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}

STEP 3

Now, plug in the given values for (x1,y1)(x1, y1) and (x2,y2)(x2, y2) into the distance formula.
Distance=(73)2+(71)2Distance = \sqrt{(7 -3)^2 + (7 -1)^2}

STEP 4

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

STEP 5

Square the numbers inside the square root.
Distance=16+36Distance = \sqrt{16 +36}

STEP 6

Add the numbers inside the square root.
Distance=52Distance = \sqrt{52}

STEP 7

implify the square root.
Distance=213Distance =2\sqrt{13}The distance between the points (3,1)(3,1) and (7,7)(7,7) is 2132\sqrt{13} units.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord