Lines And Angles

Given points:

$A(2%2C-3)$ and $B(5%2C6)$

Step 1: Use the section formula

The section formula states that if a point $P(x%2Cy)$ divides the line joining $A(x_1%2C%20y_1)$ and $B(x_2%2C%20y_2)$ in the ratio $m%3An$ , then:

$x%20%3D%20%5Cfrac%7Bm%20x_2%20%2B%20n%20x_1%7D%7Bm%2Bn%7D%2C%20%5Cquad%20y%20%3D%20%5Cfrac%7Bm%20y_2%20%2B%20n%20y_1%7D%7Bm%2Bn%7D$

Step 2: Apply the condition

The X-axis divides the line, so the y-coordinate of the dividing point is 0.

$%5Cfrac%7Bm(6)%20%2B%20n(-3)%7D%7Bm%2Bn%7D%20%3D%200$

Step 3: Solve for $m%3An$

$6m%20-%203n%20%3D%200$

$6m%20%3D%203n$

$%5Cfrac%7Bm%7D%7Bn%7D%20%3D%20%5Cfrac%7B3%7D%7B6%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D$

Final Answer: 1:2

Chapter Questions
1 MCQs