FINDING AREA OF A TRIANGLE USING COORDINATES
In Geometry, a triangle is the 3 – sided polygon which has 3 edges and 3 vertices.
Area of the triangle is a measure of the space covered by the triangle in the two-dimensional plane.
In this article, you will learn how to find the area of a triangle in the coordinate geometry.
Finding Area of a Triangle Using Coordinates :
When we have vertices of the triangle and we need to find the area of the triangle, we can use the following steps.
(i) Plot the points in a rough diagram.
(ii) Take the vertices in counter clock-wise direction. Otherwise the formula gives a negative value.
(iii) Use the formula given below
And the diagonal products x1y2, x2y3 and x3y1 as shown in the dark arrows.
Also add the diagonal products x2y1, x3y2 and x1y3 as shown in the dotted arrows.
Now, subtract the latter product from the former product to get area of the triangle ABC.
So, area of the triangle ABC is
Example 1 :
Find the area of triangle whose vertices are (-3, -9), (-1, 6) and (3, 9).
Solution :
First we have to plot the point in the graph sheet as below.
Now we have to take anticlockwise direction. So we have to take the points in the order C (3, 9) B (-1, 6) and A (-3, -9)
Area of the triangle CBA
= (1/2) {(18 + 9 - 18) - (-9 - 18 - 27)}
= (1/2) {9 - ( -54)}
= (1/2) {9 + 54}
= (1/2) (63)
= (63/2)
= 31.5 Square units.
Therefore the area of CBA = 31.5 square units.
Example 2 :
Find the area of triangle whose vertices are (-3, -9) (3, 9) and (5, -8).
Solution :
First we have to plot the point in the graph sheet as below.
Now we have to take anticlockwise direction. So we have to take the points in the order B (3, 9) A (-3, -9) and C (5, -8)
x1 = 3 x2 = -3 x3 = 5
y1 = 9 y2 = -9 y3 = -8
Area of the triangle BAC
= (1/2) {(-27 - 24 + 45) - (-27 - 45 - 24)}
= (1/2) {(-51 + 45) - (-96)}
= (1/2) {-6 + 96}
= (1/2) (90)
= (90/2)
= 45 Square units.
Therefore the area of BAC = 45 square units.
Example 3 :
Find the area of triangle whose vertices are (4, 5) (4, 2) and (-2, 2).
Solution :
Now we have to take anticlockwise direction. So we have to take the points in the order A (4, 5) C (-2, 2) and B (4, 2)
x1 = 4 x2 = -2 x3 = 4
y1 = 5 y2 = 2 y3 = 2
Area of the triangle ACB
= (1/2) {(8 - 4 + 20) - (-10 + 8 + 8)}
= (1/2) {(28 - 4) - ( -10 + 16)}
= (1/2) (24 - 6)
= (1/2) x 18
= (18/2)
= 9 Square units.
Therefore the area of ACB = 9 square units
Example 4 :
Find the area of triangle whose vertices are (3, 1) (2, 2) and (2, 0).
Solution :
Now we have to take anticlockwise direction. So we have to take the points in the order B (2, 2) C (2, 0) and A (3, 1)
x1 = 2 x2 = 2 x3 = 3
y1 = 2 y2 = 0 y3 = 1
Area of the triangle BCA
= (1/2) {(0 + 2 + 6) - (4 + 0 + 2)}
= (1/2) {8 - 6}
= (1/2) (2)
= (2/2)
= 1 Square units.
Therefore the area of ACB = 1 square units.
Example 5 :
Find the area of triangle whose vertices are (3, 1) (0, 4) and (-3, 1).
Solution :
Now we have to take anticlockwise direction. So we have to take the points in the order B (0, 4) C (-3, 1) and A (3, 1).
x1 = 0 x2 = -3 x3 = 3
y1 = 4 y2 = 1 y3 = 1
Area of the triangle BCA
= (1/2) {(0 -3 + 12) - (-12 + 3 + 0)}
= (1/2) {9 - ( -12 + 3)}
= (1/2) {9 - (-9) }
= (1/2) {9 + 9)}
= (1/2) x 18
= 9 Square units.
Therefore the area of BCA = 9 square units.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
©All rights reserved. onlinemath4all.com
Recent Articles
-
Linear vs Exponential Growth
May 23, 22 01:59 AM
Linear vs Exponential Growth - Concept - Examples
-
Exponential vs Linear Growth Worksheet
May 23, 22 01:42 AM
Exponential vs Linear Growth Worksheet
-
SAT Math Questions on Exponential vs Linear Growth
May 23, 22 01:34 AM
SAT Math Questions on Exponential vs Linear Growth
