Three points P, Q, and R lie on the line segm | vedclass

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

Question

(D) The points $P, Q,$ and $R$ divide the line segment $AB$ into four equal parts. Thus,the ratio $AR:RB$ is $3:1$.Using the section formula,if a poin

Vedclass · Accepted Answer

$(9/2, -5/2)$

Vedclass · Answer

(D) The points $P, Q,$ and $R$ divide the line segment $AB$ into four equal parts. Thus,the ratio $AR:RB$ is $3:1$.Using the section formula,if a point $(x, y)$ divides the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ in the ratio $m:n$,the coordinates are given by:$x = \frac{mx_2 + nx_1}{m+n}, y = \frac{my_2 + ny_1}{m+n}$For point $R$,$m=3$ and $n=1$,with $A(-6, 8)$ and $B(8, -6)$:$x = \frac{3(8) + 1(-6)}{3+1} = \frac{24 - 6}{4} = \frac{18}{4} = \frac{9}{2}$$y = \frac{3(-6) + 1(8)}{3+1} = \frac{-18 + 8}{4} = \frac{-10}{4} = -\frac{5}{2}$Therefore,the coordinates of $R$ are $(\frac{9}{2}, -\frac{5}{2})$.

Three points $P, Q,$ and $R$ lie on the line segment joining points $A(-6, 8)$ and $B(8, -6)$ such that $AP = PQ = QR = RB$. Find the coordinates of $R$.

Similar Questions

In what ratio does the point $(8, 4)$ divide the line segment joining the points $(5, -2)$ and $(9, 6)$?

The point on the $y$-axis equidistant from the points $(3, 2)$ and $(-1, 3)$ is

Find the coordinates of the point which divides the line segment joining the points $(a + b, a - b)$ and $(a - b, a + b)$ externally in the ratio $a : b$.

The coordinates of the points $A, B, C$ are $(x_1, y_1)$,$(x_2, y_2)$,$(x_3, y_3)$ and $D$ divides the line $AB$ in the ratio $l : k$. If $P$ divides the line $DC$ in the ratio $m : k + l$,then the coordinates of $P$ are

The distance of the midpoint of the line segment joining the points $(a \sin \theta, 0)$ and $(0, a \cos \theta)$ from the origin is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module