Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find the Value of X for Which the Points (X, −1), (2, 1) and (4, 5) Are Collinear. - Mathematics

Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.

#### Solution

Let the given points be A (x, −1), B (2, 1) and C (4, 5).
Slope of AB =  $\frac{1 + 1}{2 - x} = \frac{2}{2 - x}$

Slope of BC = $\frac{5 - 1}{4 - 2} = \frac{4}{2} = 2$

It is given that the points (x, −1), (2, 1) and (4, 5) are collinear.

$\therefore$ Slope of AB  = Slope of BC

$\Rightarrow \frac{2}{2 - x} = 2$

$\Rightarrow 1 = 2 - x$

$\Rightarrow x = 1$

Hence, the value of x is 1.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.1 | Q 18 | Page 14

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