How to find the perimeter of a triangle with coordinates

This online calculator is designed to quickly calculate a number of characteristics of a triangle by the coordinates of its vertices. You enter the coordinates of the vertices A, B, and C. The calculator calculates the following values ​​from the coordinates:

• the length of the side a - the side opposite to the vertex A
• the length of the side b - the side opposite to vertex B
• the length of the side c - the side opposite to vertex C
• the value of the angle α at the vertex A
• the value of the angle β at the vertex B
• the value of the angle γ at the vertex C
• the perimeter of the triangle
• area of ​​a triangle

If you need something else, write in the comments, we'll add it. The formulas for calculating triangle values ​​are described under the calculator.

Triangle values by coordinates of vertices

Vertex A

Vertex B

Vertex C

Calculation precision

Digits after the decimal point: 2

Calculating a triangle by the coordinates of the vertices

The lengths of the sides are found by the formula for calculating the distance between points in Cartesian coordinates

The angles are from the formulas for the dot product of vectors at the vertices.

The perimeter is found by simply adding the lengths of the sides.

The area of ​​a triangle is found through the determinant

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!.

#"to find the perimeter of the triangle we require to"#
#"calculate the lengths of the 3 sides"#

#"perimeter "=AB+AC+BC#

#color(blue)"calculate AB"#

#"Note that the points A and B have the same value of"#
#"x-coordinate which means that AB is a vertical line"#

#"Thus the length of AB is the difference in y-coordinates"#

#rArrAB=6-2=4#

#color(blue)"calculate BC"#

#"Note that the points B and C have the same value of "#
#"y-coordinate which means that BC is a horizontal line"#

#"Thus the length of BC is the difference in x-coordinates"#

#rArrBC=3-(-3)=6#

#color(blue)"calculate AC"#

#"to calculate AC use the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(-3,6)" and "(x_2,y_2)=(3,2)#

#AC=sqrt((3+3)^2+(2-6)^2)#

#color(white)(AC)=sqrt(36+16)=sqrt52#

#rArr"perimeter "=4+6+sqrt52~~17.21" to 2 dec. places"#

Find perimeter of a triangle on a coordinate plane with coordinates A(-3,6), B(-3,2) and C(3,2) rounded off to 2 decimals places.

Answer

Verified

Hint:In the given question, we need to calculate the perimeter of a triangle whose coordinates of vertices are given to us. In such types of questions, we have to first find the lengths of sides of the triangle using distance formula and then sum up the distances to find the perimeter of the required triangle.

Complete step by step answer:
Perimeter of a triangle $ = $ sum of all sides.
So, we need to find the lengths of sides, namely AB, BC and CA.
Using distance formula,
Distance between two points whose coordinates are given as\[({x_1},{y_1})\] and \[({x_2},{y_2})\] is given as $\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} $.
So, distance between A and B = $AB = \sqrt {{{( - 3 - ( - 3))}^2} + {{(2 - 6)}^2}} $
 $ = AB = \sqrt {0 + 16} $
$ = AB = 4$units
Distance between B and C = $BC = \sqrt {{{(3 - ( - 3))}^2} + {{(2 - 2)}^2}} $
 $ = BC = \sqrt {36 + 0} $
 $ = BC = 6$units
Distance between C and A = $CA = \sqrt {{{( - 3 - 3)}^2} + {{(6 - 2)}^2}} $
$ = CA = \sqrt {36 + 16} $
$ = CA = \sqrt {52} $
$ = CA = 2\sqrt {13} $
$ = CA = 2 \times 3.6055$
$ = CA = 7.21{\text{ }}$units (rounded off up to two decimal places)
So, perimeter of triangle ABC $ = AB + BC + CA$
Perimeter of triangle ABC $ = \left( {4 + 6 + 7.21} \right)$ units
Perimeter of triangle ABC $ = 17.21{\text{ }}$units.
So, the perimeter of the triangle on a coordinate plane with coordinates A(-3,6), B(-3,2) and C(3,2) rounded off to 2 decimals places is $17.21{\text{ }}$ units .

Note: The given triangle in the problem is a right angled triangle as side AB is along the x axis and side BC is along the y axis. So, the side CA can also be calculated using the Pythagoras theorem and then the perimeter of triangle ABC can be evaluated by adding up all the sides.

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