Question

14. A (2, 3) and B(-2, 5) are two given points.Find :(i) the equation of AB:​

Answer 1

Question :-

(2, 3) and B(-2, 5) are two given points.Find :(i) the equation of AB.

Answer :-

$\implies \: \red{\boxed{2y + x = 8}} \:$

To find :-

Find equation of AB.

Formula used :-

$\small \: slope\: of \: two \: points \: \: (m) \\ \\ \implies \: \boxed{m \: = \frac{ y_2 - y_1 }{ \: x_2 - x_2 } }$

Equation of two points ,

$\implies \: \boxed{y \: - y_1 = m \: ( x - x_1)} \\ \\ \bf{m \: is \: the \: slops \: of \: points \: }$

Step - by - step explanation:-

Solution :-

Given points are,

A ( 2,3) and B ( -2,5)

$\: let \: \\ x_1 = 2 \: , \: x_2 = - 2 \\ \\ y_1 = 3 \:, y_2 = 5$

Then slope(m) of these points is ,

$\implies \: {m \: = \frac{ y_2 - y_1 }{ \: x_2 - x_2 } } \: \\ \\ \implies \: m \: = \frac{5 - 3}{ - 2 - 2} \\ \\ \implies \: m \: = \frac{2}{ - 4} = \frac{ - 1}{2}$

Now equation of AB is ,

$\implies \: y \: - 3 = \frac{ - 1}{2} (x - 2) \\ \\ \implies \: 2y - 6 = - x + 2 \\ \\ \implies \: \red{\boxed{2y + x = 8}}$

This is the required equation.