No.158 Area of a Triangle on a Coordinate Plane
POINT
Calculate every coordinate from the equations. Find A by solving the two equations as a system, and find B and C by setting \(y=0\). Then use base × height ÷ 2.
Example
The sketch shows \(y=2x+4\) and \(y=-x+10\). Their intersection is A, and their x-axis intersections are B and C. Each grid square represents 1 unit. Calculate the area of triangle ABC.
Find A, B and C by calculation, then find the area.
\(A=(2,8),\ B=(-2,0),\ C=(10,0)\)
Area \(=\frac12\times12\times8=48\).
Area \(=\frac12\times12\times8=48\).
TRY
TRY 1
For \(y=x+3\) and \(y=-2x+9\), let their intersection be A and their x-axis intersections be B and C. Find the area of triangle ABC.
\(A=(2,5), B=(-3,0), C=(\frac92,0)\). Area \(=\frac{75}{4}\).
TRY 2
For \(y=2x+2\) and \(y=-x+8\), define A, B and C in the same way. Find the area.
\(A=(2,6), B=(-1,0), C=(8,0)\). Area \(=27\).