In what ratio does the line 3x + 4y = 7 divid | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the line $3x + 4y - 7 = 0$ divide the segment joining $A(1, 2)$ and $B(-2, 1)$ in the ratio $k:1$.Using the section formula,the coordinates of

Vedclass · Accepted Answer

$4:9$

Vedclass · Answer

(A) Let the line $3x + 4y - 7 = 0$ divide the segment joining $A(1, 2)$ and $B(-2, 1)$ in the ratio $k:1$.Using the section formula,the coordinates of the point of division are $\left( \frac{-2k + 1}{k+1}, \frac{k + 2}{k+1} \right)$.Since this point lies on the line $3x + 4y = 7$,we substitute these coordinates into the equation:$3\left( \frac{-2k + 1}{k+1} \right) + 4\left( \frac{k + 2}{k+1} \right) = 7$$3(-2k + 1) + 4(k + 2) = 7(k + 1)$$-6k + 3 + 4k + 8 = 7k + 7$$-2k + 11 = 7k + 7$$4 = 9k$$k = \frac{4}{9}$Thus,the ratio is $4:9$.

In what ratio does the line $3x + 4y = 7$ divide the line segment joining the points $(1, 2)$ and $(-2, 1)$?

Similar Questions

Let $A = (a_1, a_2)$ and $B = (b_1, b_2)$ be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between $A$ and $B$?

The inclination of the straight line passing through the point $(-3, 6)$ and the midpoint of the line joining the points $(4, -5)$ and $(-2, 9)$ is

The points $A(1, 1)$,$B(-2, 7)$,and $C(3, -3)$ are . . . . . . .

$P$ and $Q$ are points on the line joining $A,(-2, 5)$ and $B,(3, 1)$ such that $AP = PQ = QB$. Then the mid-point of $PQ$ is

The distance between the points $(7, 5)$ and $(3, 2)$ is equal to ........... $unit$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module