1.

Find the equations to the sides of the triangles the coordinates of whose angular points are respectively: (1,4), (2, - 3) and (-1, - 2)

Answer»

Given: 

Points A (1, 4), B(2, -3) and C(-1, -2). 

Assuming: 

m1, m2, and m3 be the slope of the sides AB, BC and CA, respectively. 

Concept Used:

The slope of the line passing through the two points ( x1, y1) and ( x2, y2). The equation of the line passing through the two points ( x1, y1) and ( x2, y2). 

To find: 

The equation of sides of the triangle. 

Explanation:

m1 = \(\frac{-3-4}{2-1}\) ,  m2 = \(\frac{-2+3}{-1-2}\) ,​​​​m3 = \(\frac{4+2}{1+1}\)

m1 = -7, m2 =  \(\frac{1}{3}\) and m3 = 3 

So, the equation of the sides AB, BC and CA are 

Formula used: y – y1= m (x – x1) 

y – 4 = -7 (x – 1), y + 3 = 

 \(\frac{1}{3}\) (x - 2) and y + 2 = 3(x+1) 

⇒ 7x + y =11, x+ 3y +7 =0 and 3x – y +1 = 0 

Hence, equation of sides are 7x + y =11, x+ 3y +7 =0 and 3x – y +1 = 0


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