Question -
Answer -
Given (x, 4), (2, -6)and (5, 4) are the vertices of a triangle.
We have the conditionthat three points to be collinear, the area of the triangle formed by thesepoints will be zero. Now, we know that, vertices of a triangle are (x1,y1), (x2, y2) and (x3, y3),then the area of the triangle is given by,
тЗТ┬а[x (тАУ 10) тАУ 4(тАУ3) + 1(8 тАУ 30)] = ┬▒ 70
тЗТ┬а[тАУ 10x + 12 +38] = ┬▒ 70
тЗТ┬а┬▒70 = тАУ 10x + 50
Taking positive sign,we get
тЗТ┬а+ 70 = тАУ 10x +50
тЗТ┬а10x = тАУ 20
тЗТ┬аx = тАУ 2
Taking тАУnegative sign,we get
тЗТ┬атАУ 70 = тАУ 10x +50
тЗТ┬а10x = 120
тЗТ┬аx = 12
Thus x = тАУ 2, 12