Find the coordinates of the points of trisect | vedclass

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

Question

(A) Let $A = (4, -1)$ and $B = (-2, -3)$. Let $P$ and $Q$ be the points of trisection such that $AP = PQ = QB$.Point $P$ divides $AB$ in the ratio $1:

Vedclass · Accepted Answer

$(2, -5/3)$ and $(0, -7/3)$

Vedclass · Answer

(A) Let $A = (4, -1)$ and $B = (-2, -3)$. Let $P$ and $Q$ be the points of trisection such that $AP = PQ = QB$.Point $P$ divides $AB$ in the ratio $1:2$. Using the section formula $\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)$:$x_1 = \frac{1(-2) + 2(4)}{1+2} = \frac{-2+8}{3} = \frac{6}{3} = 2$$y_1 = \frac{1(-3) + 2(-1)}{1+2} = \frac{-3-2}{3} = -\frac{5}{3}$So,$P = (2, -5/3)$.Point $Q$ divides $AB$ in the ratio $2:1$. Using the section formula:$x_2 = \frac{2(-2) + 1(4)}{2+1} = \frac{-4+4}{3} = 0$$y_2 = \frac{2(-3) + 1(-1)}{2+1} = \frac{-6-1}{3} = -\frac{7}{3}$So,$Q = (0, -7/3)$.

Find the coordinates of the points of trisection of the line segment joining $(4, -1)$ and $(-2, -3)$.

Similar Questions

Find the coordinates of the point which divides the line segment joining the points $(-1, 7)$ and $(4, -3)$ in the ratio $2:3$.

Find the area of a triangle formed by the points $A(5, 2)$,$B(4, 7)$,and $C(7, -4)$ (in square units).

If $A$ and $B$ are $(-2, -2)$ and $(2, -4)$ respectively,find the coordinates of $P$ such that $AP = \frac{3}{7} AB$ and $P$ lies on the line segment $AB$.

Find the centre of a circle passing through the points $(6, -6), (3, -7)$ and $(3, 3)$.

Find the point on the $x$-axis which is equidistant from $(2, -5)$ and $(-2, 9).$

Vedclass Test Series

Exam Paper Generator

Online Exam Module