Question

if (5.7),(3.p)and (6.6) are colliner then the value of p is​

Answer 1

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Answer 2

Answer:

p = 9

Step-by-step explanation:

if the points are collinear then the slope or tanθ value for the lines joining them to each other must be the same so,

For the line joining points (5,7) and (3,p) -

Slope of line, say m1 = $\frac{y2 - y1}{x2 - x1}$ = $\frac{p-7}{3-5}$ = $\frac{p-7}{-2}$

similarly, for the line joining points (3,p) and (6,6) -

Slope of line m2 = \frac{y2 - y1}{x2 - x1} = $\frac{6-p}{6-3}$ = $\frac{6-p}{3}$

Now for the points to be collinear as stated before,

m1 = m2 must hold, that is the slopes must be equal

∴  \frac{p-7}{-2} = \frac{6-p}{3}

⇒  3p - 21 = -12 + 2p

⇒ p = 9