Question

Equation of the line with slope 1/3 and divides the line joining the points (0, 2) and (5, -3) in the ratio 4:7 is​

Answer 1

Answer:

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Answer 2

Equation of line is $\bf \red{ 11x - 33y - 14 = 0}$

Given:

• A line with slope 1/3 and ,
• Divides the line joining the points (0, 2) and (5, -3) in the ratio 4:7 .

To find:

• Find equation of line.

Solution:

Formula to be used:

1. Equation of line having slope m and passing through (x1,y1):$\bf (y - y_1) = m(x - x_1)$
2. Section formula:If a point divides a line segment (internally) having end points as (x1,y1) and (x2,y2), in m:n, then coordinates of point P(x,y) is given by $\bf x = \frac{mx2 + nx1}{m + n}$, $\bf y= \frac{my2 + ny1}{m + n}$

Step 1:

Find the point of intersection of line and line segment; because it passes through that point, let the point is P.

Here points are (0,2) and (5,-3)

Ratio of division is 4:7

Thus,

Coordinates of P are

$x = \frac{4( 5) + 7(0)}{4 + 7}$

or

$\bf x = \frac{20}{11}$

and

$y = \frac{4( - 3) + 7 \times 2}{11}$

or

$y = \frac{ - 12+ 14}{11}$

or

$\bf y = \frac{2}{11}$

Thus,

The point P(20/11,2/11)

Step 2:

Find the equation of line.

Line passes through P(20/11,2/11)

Slope m= 1/3

Equation of line:$y - \frac{2}{11} = \frac{1}{3} (x - \frac{20}{11} )$

or

$11y - 2 = \frac{1}{3} (11x - 20)$

or

$33y - 6 = 11x - 20$

or

$- 11x + 33y - 6 + 20 = 0$

or

$11x - 33y - 14 = 0$

Thus,

Equation of line is $\bf 11x - 33y - 14 = 0$

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