The locus of a point which moves such that th | vedclass

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

Question

(D) Let the point be $P(x, y)$. The vertices of the triangle are $A(1, 2)$,$B(-2, 5)$,and $P(x, y)$.The area of the triangle is given by the formula:

Vedclass · Accepted Answer

$3x + 3y + 7 = 0 \quad \& \quad 3x + 3y - 25 = 0$

Vedclass · Answer

(D) Let the point be $P(x, y)$. The vertices of the triangle are $A(1, 2)$,$B(-2, 5)$,and $P(x, y)$.The area of the triangle is given by the formula: $	ext{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$.Substituting the values: $8 = \frac{1}{2} |1(5 - y) + (-2)(y - 2) + x(2 - 5)|$.$16 = |5 - y - 2y + 4 - 3x| = |9 - 3y - 3x|$.$16 = |9 - 3(x + y)|$.This gives two cases:Case $1$: $9 - 3(x + y) = 16 \implies -3(x + y) = 7 \implies 3x + 3y + 7 = 0$.Case $2$: $9 - 3(x + y) = -16 \implies -3(x + y) = -25 \implies 3x + 3y - 25 = 0$.Thus,the locus is $3x + 3y + 7 = 0$ and $3x + 3y - 25 = 0$.

The locus of a point which moves such that the area of the triangle formed by it with the vertices $(1, 2)$ and $(-2, 5)$ is $8$ sq. units is/are

Similar Questions

$A$ ray of light passing through the point $A(1, 2)$ is reflected at a point $B$ on the $x$-axis and then passes through $(5, 3)$. Then the equation of $AB$ is:

Let $A$ be the set of all points $(\alpha, \beta)$ such that the area of the triangle formed by the points $(5, 6), (3, 2),$ and $(\alpha, \beta)$ is $12 \text{ square units}.$ Then the least possible length of a line segment joining the origin to a point in $A$ is:

The locus of the point $P$ which is equidistant from $3x + 4y + 5 = 0$ and $9x + 12y + 7 = 0$ is:

$A$ ray of light coming from the point $(1, 2)$ is reflected at a point $A$ on the $x$-axis and then passes through the point $(5, 3)$. The coordinates of the point $A$ are

The line $AB$ cuts off equal intercepts $2a$ from the axes. From any point $P$ on the line $AB$, perpendiculars $PR$ and $PS$ are drawn to the axes. The locus of the mid-point of $RS$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module