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▴=\frac{1}{2}\left\{ x_{1}(y_{2}-y_{3})+ x_{2}(y_{3}-y_{1})+ x_{3}(y_{1}-y_{3})\right\} 

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Class 10: Co-ordinate Geometry-Area of Triangles

- BENNY VARGHESE
PGT Mathematics
JNV Pathanamthitta
KERALA-686511

Verification

Objectives

To find the area of a triangle knowing 
its vertices and to verify the same by
using base and altitude

Drag the points A,B,C to change vertices 
of the triangle ABC and click “Start Animation”
button. using the formula given for area 
compute it and type in your answer in the
input box against “Your Ans Plz >>” and 
press enter button in the keyboard. 
Follow the instructions carefully

How to proceed?

C = (7, 0)
B = (1, 0)
A = (3, 3)
InputBox1 = Textfield(ans)
a = Area(A, B, C)
mm: 8
b = If(mm ≟ a, true, false)
c = 0.8 (slider from 0.8 to 5)
d: x(A)
e: x(B)
f: x(C)
g: y(A)
h: y(B)
i: y(C)
text4: "\frac{1}{2}\left\{(" + (LaTeX[d]) + ")(" + (LaTeX[h]) + "-" + (LaTeX[i]) + ")+(" + (LaTeX[e]) + ")(" + (LaTeX[i]) + "-" + (LaTeX[g]) + ")+(" + (LaTeX[f]) + ")(" + (LaTeX[g]) + "-" + (LaTeX[h]) + ")
 \right\} =" + (LaTeX[a]) + " \; sq. \; units"
j = false
A' = Dilate(A, If[1 < c < 2, 2 - c, 0], B)
k = Segment(A, A')
B' = Dilate(B, If[2 < c < 3, 3 - c, 0], C)
l = Segment(B, B')
C' = Dilate(C, If[3 < c < 4, 4 - c, 0], A)
m = Segment(C, C')
n = OrthogonalLine(A, l)
D = Intersect(l, n)
A'_1 = Dilate(A, If[4 < c < 5, 5 - c, 0], D)
p = Segment(A, A'_1)
α = Angle(C, D, A)
o = true
q = false
BC = Distance(B, C)
AD = Distance(A, D)
r = Segment(B, C)
s = Segment(A, D)
text7: "▴=\frac{1}{2}(BC)(AD)=\frac{1}{2}(" + (LaTeX[r]) + ")(" + (LaTeX[s]) + ")=" + (LaTeX[a]) + " \; sq.units"
t = false
u: false