If P(1, 12) divides the line segment overline | vedclass

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

Question

(A) Let the coordinates of $B$ be $(x, y)$.Given that $P(1, 12)$ divides the line segment $AB$ in the ratio $m:n = 2:1$,where $A(x_1, y_1) = (3, 8)$ a

Vedclass · Accepted Answer

$(0, 14)$

Vedclass · Answer

(A) Let the coordinates of $B$ be $(x, y)$.Given that $P(1, 12)$ divides the line segment $AB$ in the ratio $m:n = 2:1$,where $A(x_1, y_1) = (3, 8)$ and $B(x_2, y_2) = (x, y)$.Using the section formula: $P(x, y) = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)$.Substituting the values: $1 = \frac{2(x) + 1(3)}{2+1} \implies 1 = \frac{2x + 3}{3} \implies 3 = 2x + 3 \implies 2x = 0 \implies x = 0$.Similarly,$12 = \frac{2(y) + 1(8)}{2+1} \implies 12 = \frac{2y + 8}{3} \implies 36 = 2y + 8 \implies 2y = 28 \implies y = 14$.Thus,the coordinates of $B$ are $(0, 14)$.

$1$. $\square ABCD$ is a rhombus.	$a$. $\overline{AC}$ and $\overline{BD}$ bisect each other.
$2$. $\square ABCD$ is a parallelogram.	$b$. $\overline{AC}$ and $\overline{BD}$ bisect each other at right angles.
$3$. $\square ABCD$ is a rectangle.	$c$. $\overline{AC}$ and $\overline{BD}$ are congruent and bisect each other at right angles.
$4$. $\square ABCD$ is a square.	$d$. $\overline{AC}$ and $\overline{BD}$ are congruent and bisect each other.

If $P(1, 12)$ divides the line segment $\overline{AB}$ starting from $A$ in the ratio $2:1$ and $A(3, 8)$,then the coordinates of $B$ are $\ldots \ldots$

Similar Questions

If the distance between points $A(a, 2)$ and $B(3, -5)$ is $\sqrt{53},$ find the possible values of $a$.

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 $\Delta PAB = 4$.

If $A(6, 5)$ and $B(4, 3)$,then the midpoint of $\overline{AB}$ is..........

Obtain the circumcentre of $\Delta ABC$ with vertices $A (-3, -1)$,$B (-1, 3)$ and $C (6, 2)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module