Question

using slopes show that the points a(6 -1) b(5 0) and c(2 3) are collinear......... plz answer fast​

Answer 1

SOLUTION :

TO PROVE

The points A(6, -1), B(5, 0) and C (2, 3) are collinear using slopes

FORMULA TO BE IMPLEMENTED

The slope of the line joining the points ( x, y) & (a, b) is given by

$\displaystyle \sf{m} = \frac{b - y}{a - x}$

PROOF

The slope of the line joining the points A & B is

$\displaystyle \sf{ \: } m_1 = \frac{0 + 1}{5 - 6} = - 1$

The slope of the line joining the points B & C is

$\displaystyle \sf{ \: } m_2 = \frac{3 - 0}{2 - 5} = \frac{3}{ - 3} = - 1$

The slope of the line joining the points A & C is

$\displaystyle \sf{ \: } m_3 = \frac{3 + 1}{2 - 6} = \frac{4}{ - 4} = - 1$

$\sf{ \therefore \: \: \: m_1= m_2 =m_3}$

Hence three given points A(6, -1), B(5, 0) and C (2, 3) are collinear

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