Question

find the equation of the straight line which passes through the points (-4,5) and (-2,3) and also find the length intercepted between co-ordinate axes.​

Answer 1

Question :-

• Find the equation of the straight line which passes through the points (-4,5) and (-2,3) and also find the length intercepted between co-ordinate axes.

Answer

Given :-

• A line passes through the points (- 4, 5) and (- 2, 3).

To Find :-

• Equation of line
• The length intercepted between co-ordinate axes.

Formula used :-

Let us consider a line which passes through two loints A and B, then equation of line AB is given by

$\bf \:y - y_1 = \dfrac{y_2-y_1}{x_2-x_1} (x-x_1)$

Solution :-

A line passes through the points (- 4, 5) and (- 2, 3).

So, required equation of line is

$\bf \:y - y_1 = \dfrac{y_2-y_1}{x_2-x_1} (x-x_1)$

where,

$\bf \:x_1 = - 4 ,y_1 =5, x_2 - 2= , y_2 =3$

$\bf\implies \:\bf \:y - 5 = \dfrac{3 - 5}{ - 2 + 4} (x + 2)$

$\bf\implies \:y - 5 = - 1(x + 2)$

$\bf\implies \:y - 5 = - x - 2$

$\bf\implies \:x + y = 3$

is the required equation of line.

To find the length of line intercepted between the axis.

x + y = 3

● Point of interestion with x - axis.

Put y = 0, we get x = 3.

So, coordinate is C(3, 0)

● Point of intersection with y - axis.

Pur x = 0, we get y = 3

So, coordinate is D(0, 3).

$\bf \:Length \: of \: intercept = CD$

$\bf\implies \ CD = \sqrt{ {(3 - 0)}^{2} + {(0 - 3)}^{2} }$

$\bf\implies \:CD = \sqrt{9 + 9} = \sqrt{18}$

$\bf\implies \: CD = 3 \sqrt{2} \: units$

Answer 2

Answer:

this is correct........................