Question

If the points (1,4),(3,-2) and (p,-5) lie on a line,find the value of p

Answer 1

Answer:

p = 4

Step-by-step explanation:

Given points are A(1,4), B(3,-2) and C(p,-5)

Slope of AC:

m₁ = (y₂ - y₁)/(x₂ - x₁)

    = (-5 - 4)/(p - 1)

    = -9/(p - 1)

Slope of BC:

m₂ = (y₂ - y₁)/(x₂ - x₁)

    = (-5 + 2)/(p - 3)

    = (-3)/(p - 3)

Now,

Slope of AC = Slope of BC

⇒ -9/(p - 1) = (-3)/(p - 3)

⇒ -9(p - 3) = (-3)(p - 1)

⇒ -9p + 27 = -3p + 3

⇒ -9p +  3p = 3 - 27

⇒ -6p = -24

⇒ p = 4.

Therefore, the value of p = 4.

Hope it helps!

Answer 2

Answer:

p=4

Step-by-step explanation:

m1(AC)=(-5-4)/(p-1)

=-9/(p-1)

m2(BC)=(-5+2)/(p-3)

=(-3)/(p-3)

NOW AS WE KNOW THAT IN A ST. LINE IF POINTS LIE THEN

m1=m2

=>-9/(p-1)=(-3)/(p-3)

=>-9p+27=-3p+3

=>-6p=-24

=>p=4

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