Question

The area of a triangle is 5 sq.units. Two of its vertices are (2,1) and (3,-2). The third
vertex lies on the line y=x+3. Find the third vertex.​

Answer 1

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Answer 2

Step-by-step explanation:

For Triangle -->

Area = 1/2 {x1(y2-y3)+x2(y3-y1)+x3(y1-y2)}

5 = 1/2 { 2(-2-y3)+3(y3-1)+x3(1+2)}

10 = -2(2+y3) + 3(y3-1) + 3x3

-4 - 2y3 + 3y3 - 3 + 3x3 = 10

3x3 + y3 = 17 -------(1)

x3 - y3 = -3 --------(2) (already given)

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4x3 = 14

x3 = 14/4 = 7/2

3(7/2) + y3 = 17

y3 = 17 - 21/2 = 13/2

Third vertex is ( 7/2 , 13/2 )