Question

if the point (1,2) (-5,6) and (p,-2 ) are collinear, then p =​

Answer 1

Answer:

The value of p is -17.

Step-by-step explanation:

Since we have given that

points (1, 2), (- 5,6) and (p, - 2) are collinear,

So, Slope of (1,2) and (-5,6) would be

\dfrac{6-2}{-5-1}=\dfrac{4}{-6}=\dfrac{2}{-3}

−5−1

6−2

=

−6

4

=

−3

2

Slope of (-5,6) and (p,-2) would be

\dfrac{-2-6}{p+5}=\dfrac{-8}{p+5}

p+5

−2−6

=

p+5

−8

Since the points are collinear , so their slopes should be equal to each other.

So, it becomes,

$$\begin{lgathered}\dfrac{2}{-3}=\dfrac{-8}{p+5}\\\\2(p+5)=-3\times -8\\\\2p+10=-24\\\\2p=-24-10\\\\2p=-34\\\\p=\dfrac{-34}{2}\\\\p=-17\end{lgathered}$$

Hence, the value of p is -17.

# learn more:

If the point (-5,1), (1,p) and (4,-2)are collinear, then find the value of p

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Answer 2

Answer: The value of p is 7.

Step-by-step explanation:

If three points are collinear, then they lie on the same line. Therefore, the slope of the line passing through any two of these points will be the same as the slope of the line passing through the third point and one of the other two points.

Let's find the slope of the line passing through the points (1, 2) and (-5, 6).

Slope = (y2 - y1) / (x2 - x1)

= (6 - 2) / (-5 - 1)

= 4 / -6

= -2/3

Now, we know that the point (p, -2) lies on the same line passing through (1, 2) and (-5, 6). So, the slope of the line passing through (1, 2) and (p, -2) must be equal to -2/3.

Slope = (y2 - y1) / (x2 - x1) = (-2 - 2) / (p - 1) = -4 / (p - 1)

We can equate the two slopes and solve for p as follows:

-2/3 = -4 / (p - 1)

Multiplying both sides by (p - 1), we get:

-2(p - 1) / 3 = -4

Simplifying and solving for p, we get:

p - 1 = 6

p = 7

Therefore, the value of p is 7.

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