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Question

# Using slope concept, check whether the following points are collinear. A(7, 8), B(−5, 2) and C(3, 6).

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Solution

## The given points are A(7, 8), B(−5, 2) and C(3, 6). Here, x1 = 7, y1 = 8, x2 = −5, y2 = 2, x3 = 3 and y3 = 6 Now, we will find the slopes of the AB and BC. $\mathrm{Slope}\mathrm{of}AB=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\phantom{\rule{0ex}{0ex}}=\frac{2-8}{-5-7}\phantom{\rule{0ex}{0ex}}=\frac{6}{12}\phantom{\rule{0ex}{0ex}}=\frac{1}{2}$ $\mathrm{Slope}\mathrm{of}BC=\frac{{y}_{3}-{y}_{2}}{{x}_{3}-{x}_{2}}\phantom{\rule{0ex}{0ex}}=\frac{6-2}{3-\left(-5\right)}\phantom{\rule{0ex}{0ex}}=\frac{4}{8}\phantom{\rule{0ex}{0ex}}=\frac{1}{2}$ Here, the slope of AB is the same that of BC and point B is common to both AB and BC. ∴ Points A, B and C are collinear.

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