Question

Check whether (5 -2) (6 4) and (7 -2) are the vertices of a triangle

Answer 1

If they are vertices of a traingle then there area must not equal 0,

Area of 3 points when joined is,

1/2 |x1(y2-y3) + x2(y3 - y1) + x3(y1-y2) |,

|x| represents modulus of x,

here according to the data,

x1 = 5, y1 = -2,
x2 = 6,. y2 = 4,
x3 = 7,. y3 = -2,

Substitute this values in the above formula,

1/2 |( (5(6)) + (6(0)) + (7(-6))|,

1/2 | 30 + 0 - 42 |,

1/2 | -12|,

1/2 (12) = 6 unit²,

Here we got area = 6, which is not equals to 0,

So these are the vertices of the traingle,

If they are not vertices of traingle, then the points should be collinear so then the area must be equals to 0, if the points are not vertices of traingle,


And hence these are vertices of traingle,

Hope you understand !!