To find the distance between two points, find the change in x and y and use them as a and b in the Pythagorean theorem: √[a² + b²]. To find a shape's perimeter, add up all the distances between its corners!. Ashley F. 2 Answers By Expert Tutors The side lengths are the lengths of the line segments AB, BC, and CA. These may be found using the endpoints of the segments with the distance formula: The distance from point P(x1,y1) to point Q(x2,y2) is: Distance = √ ( (x2 - x1)2 + (y2 - y1)2 ) It is a good learning exercise to plug in all the numbers. Then, you will realize that some x-values or y-values are the same (you would also see this if you graphed the triangle). AB = 3 BC = 5 CA = 4 Also, note that 3-4-5 are integer side lengths for a right triangle. The integer triples that satisfy the Pythagorean Theorem are called Pythagorean Triples. They appear in many, many homework problems and in standardized tests. Perimeter= 3 + 5 + 4 = 12
Ben W. answered • 03/20/20 Energetic and Committed Elementary/Middle School Math Tutor
To find the perimeter of the triangle, find the lengths of each side of the triangle using the distance formula. Use the distance formula to find the length between point A and B, B and C, C and A. Then add all three lengths together to get the perimeter. Distance formula: Points A and B: d = √(-2 +5)2 + (-2 + 2)2 d = √ 32 + 0 d = √9 d = 3 Points B and C: d = √ (-5 + 2)2 + (2 +2)2 d = √ -32 + 42 d = √ 25 d = 5 Points C and A: d = √ (-5 + 5)2 + (-2 -2)2 d = √ 0 + -42 d = √ 16 d = 4 Perimeter= 3 + 5 + 4 = 12 Omni's perimeter of a triangle with vertices calculator is here for everyone who has ever wondered how to find the perimeter of a triangle with coordinates. In the article below we will not only give you the formula for the perimeter of a triangle with vertices but also explain why this formula holds so that you'll be able to compute by hand the perimeter of a triangle whose vertices are given if you ever find yourself in such a math emergency. (Under normal circumstances, though, we hope you'll keep using our perimeter of a triangle with vertices calculator!) Ready? Let's go!
As you surely remember, the perimeter of a triangle is just the distance around its edges. To find the perimeter we need to sum the lengths of our triangle's sides. So what is the perimeter of a triangle with vertices? This phrase refers to the problem where you don't know the lengths of the triangle's sides, but you only know the coordinates of the triangle's vertices. More calculations are then needed because we have to compute the side lengths from these coordinates. In what follows we'll show you how to do it.
Finding the perimeter of a triangle with vertices is not complicated, yet requires an intermediate step: we need to compute the length of each side. We do it using the distance formula. Let's say our vertices are (x1,y1)(x_1, y_1)(x1,y1), (x2,y2)(x_2, y_2)(x2,y2), (x3,y3)(x_3, y_3)(x3,y3). Then the lengths of the sides ABABAB, ACACAC, BCBCBC, respectively, read: Side AB=(x1−x2)2+(y1−y2)2Side AC=(x1−x3)2+(y1−y3)2Side BC=(x2−x3)2+(y2−y3)2\footnotesize \begin{align*} & \textrm{Side } AB = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \\ & \textrm{Side } AC = \sqrt{(x_1-x_3)^2+(y_1-y_3)^2} \\ & \textrm{Side } BC = \sqrt{(x_2-x_3)^2+(y_2-y_3)^2} \end{align*}Side AB=(x1−x2)2+(y1−y2)2Side AC=(x1−x3)2+(y1−y3)2Side BC=(x2−x3)2+(y2−y3)2 Now we sum the three lengths to determine the perimeter using three vertices: P=Side AB+Side AC+Side BC\footnotesize P = \textrm{Side } AB + \textrm{Side } AC + \textrm{Side } BCP=Side AB+Side AC+Side BC That's it! We've just determined the perimeter of a triangle with coordinates.
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This phrase means the standard triangle perimeter when we have to compute it using the coordinates of the triangle's vertices via the distance formula (Pythagorean theorem). |