By adding 5x + 2y, -7x + y, we get
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ANSWER
Three sides of a triangle have been given. We find the intersection of these lines, taking two at a time to obtain the vertices and hence the area.
x+8y−22=0 ...(1)
5x+2y−34=0 ...(2)
2x−3y+13=0 ...(3)
Multiplying equation (2) by 4 and subtracting that from equation (1), we have
x+8y−22−(20x+8y−136)=0
⇒−19x+114=0
⇒x=6 and correspondingly y=2
Next, multiplying equation (2) by 3 and equation (3) by 2 and adding the two, we have
15x+6y−102+(4x−6y+26)=0
⇒19x−76=0 or x=4
⇒20+2y−34=0
⇒y=7
Third, multiplying equation (1) by 2 and subtracting equation (3) from this, we have
2x+16y−44−(2x−3y+13)=0
⇒2x+16y−44−2x+3y−13=0
⇒19y−57=0 or y=3
⇒2x−9+13=0 or x=−2
The three vertices thus become (6,2),(4,7),(−2,3)
The area of the triangle thus becomes 21×[6×7+4×3+(−2)×2−(2×4+7×(−2)+6×3)]
=21×[42+12−4−(8−14+18)]
=21×[50−12]
=19 sq unit