A (3, 3) and B (6, 1) are the given points. F | vedclass

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

Question

(A) Given points are $A(3, 3)$ and $B(6, 1)$.Let the coordinates of point $C$ be $(x, y)$.The condition $A-B-C$ implies that $B$ lies between $A$ and

Vedclass · Accepted Answer

$(15, -5)$

Vedclass · Answer

(A) Given points are $A(3, 3)$ and $B(6, 1)$.Let the coordinates of point $C$ be $(x, y)$.The condition $A-B-C$ implies that $B$ lies between $A$ and $C$.The condition $3 AB = BC$ implies that the ratio $AB : BC = 1 : 3$.Since $B$ divides $AC$ externally in the ratio $1 : 3$ (or internally in the ratio $1 : 3$ if we consider $B$ as a point on the segment $AC$),we use the section formula.Alternatively,using vectors: $\vec{B} - \vec{A} = (6-3, 1-3) = (3, -2)$.Since $BC = 3 AB$,the vector $\vec{BC} = 3 \vec{AB} = 3(3, -2) = (9, -6)$.Thus,$\vec{C} = \vec{B} + \vec{BC} = (6, 1) + (9, -6) = (15, -5)$.

$A (3, 3)$ and $B (6, 1)$ are the given points. Find the point $C$ on the line $\overleftrightarrow{AB}$ such that $A-B-C$ and $3 AB = BC$.

Similar Questions

The mid-point of the line segment joining the points $A(-2, 8)$ and $B(-6, -4)$ is

The point which lies on the perpendicular bisector of the line segment joining the points $A (-2,-5)$ and $B (2,5)$ is

$AOBC$ is a rectangle whose three vertices are $A (0, 3)$,$O (0, 0)$,and $B (5, 0)$. The length of its diagonal is

Points $A$ and $B$ have coordinates $(2, 2)$ and $(6, 6)$. Find the coordinates of a point $P$ such that $PA = PB$ and the area of $\Delta PAB = 4$.

Find the points of trisection of the line segment joining $(7, 5)$ and $(-2, -1)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module