Question

if the points (-1,-4)(b,-2) and (5,-1) are collinear, find b​

Answer 1

Answer:

b = 3

‎

Step-by-step explanation:

Collinear points refer to those points that lie on the same line, when these points are joined, the area formed by them is 0.

‎‎

For any three points (x₁, y₁), (x₂, y₂) and (x₃, y₃), the area formed by them is given by;

‎

$\boxed{\sf Area \ of \ the \ \Delta = \dfrac{1}{2}\bigg\{\sf x_1\left(y_2 - y_3\right) + x_2\left(y_3 - y_1\right) + x_3\left(y_1 - y_2\right)\bigg\}}$

‎

Here, Area = 0 as we discussed above. We'll substitute the values of the coordinates given in the question in the formula to find the value of 'b'.

‎‎

Where;

• x₁ = -1

• x₂ = b

• x₃ = 5

• y₁ = -4

• y₂ = -2

• y₃ = -1

‎

We know that;

‎

$\dashrightarrow \ \sf Area \ of \ the \ \Delta = \dfrac{1}{2}\bigg\{\sf x_1\left(y_2 - y_3\right) + x_2\left(y_3 - y_1\right) + x_3\left(y_1 - y_2\right)\bigg\}$

‎

$\dashrightarrow \ \sf 0 = \dfrac{1}{2}\bigg\{\sf -1\left(-2 - (-1)\right) + b\left(-1 - (-4)\right) + 5\left(-4 - (-2)\right)\bigg\}$

‎

$\dashrightarrow \ \sf 0 \times 2 = \bigg\{\sf -1\left(-2 + 1\right) + b\left(-1 + 4\right) + 5\left(-4 + 2\right)\bigg\}$

‎

$\dashrightarrow \ \sf 0 = -1\left(-1\right) + b\left(3\right) + 5\left(-2\right)$

‎

$\dashrightarrow \ \sf 0 = 1 + 3b + (-10)$

‎

$\dashrightarrow \ \sf 0 = 1 + 3b - 10$

‎

$\dashrightarrow \ \sf 0 = 3b - 9$

‎

$\dashrightarrow \ \sf 3b = 9$

‎

$\dashrightarrow \ \sf b = \dfrac{9}{3}$

‎

$\dashrightarrow \ \sf b = 3$

‎

∴ The value of 'b' is 3.

Answer 2

Answer:

$:\implies$b = 3.

hope it helps uh :)