If the image of point P(2, 3) in a line L is | vedclass

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

Question

(D) Mid-point of $P(2, 3)$ and $Q(4, 5)$ is $(\frac{2+4}{2}, \frac{3+5}{2}) = (3, 4)$.Slope of $PQ = \frac{5-3}{4-2} = \frac{2}{2} = 1$.Since the line

Vedclass · Accepted Answer

$(7, 7)$

Vedclass · Answer

(D) Mid-point of $P(2, 3)$ and $Q(4, 5)$ is $(\frac{2+4}{2}, \frac{3+5}{2}) = (3, 4)$.Slope of $PQ = \frac{5-3}{4-2} = \frac{2}{2} = 1$.Since the line $L$ is the perpendicular bisector of $PQ$,the slope of line $L$ is $m = -1$.The equation of line $L$ passing through $(3, 4)$ with slope $-1$ is $y - 4 = -1(x - 3) \Rightarrow x + y - 7 = 0$.Let the image of point $R(0, 0)$ be $S(x_1, y_1)$.The mid-point of $RS$ is $(\frac{x_1}{2}, \frac{y_1}{2})$,which lies on line $L$,so $\frac{x_1}{2} + \frac{y_1}{2} - 7 = 0 \Rightarrow x_1 + y_1 = 14$.The slope of $RS$ is $\frac{y_1}{x_1}$. Since $RS \perp L$,the slope of $RS$ must be $1$ (negative reciprocal of $-1$).Thus,$\frac{y_1}{x_1} = 1 \Rightarrow x_1 = y_1$.Substituting $x_1 = y_1$ into $x_1 + y_1 = 14$,we get $2x_1 = 14 \Rightarrow x_1 = 7$ and $y_1 = 7$.Therefore,the image of $R$ is $(7, 7)$.

If the image of point $P(2, 3)$ in a line $L$ is $Q(4, 5)$,then the image of point $R(0, 0)$ in the same line is

Similar Questions

The value of $a$ for which the image of the point $(a, a - 1)$ with respect to the line mirror $3x + y = 6a$ is the point $(a^2 + 1, a)$ is:

If $A$ and $B$ are two points on the line $3x + 4y + 15 = 0$ such that $OA = OB = 9$ units,then the area of the triangle $OAB$ is

If the coordinates of the points $A, B, C$ are $(-1, 5), (0, 0)$ and $(2, 2)$ respectively and $D$ is the midpoint of $BC$,then the equation of the perpendicular drawn from $B$ to the line $AD$ is

If the perpendicular drawn from the point $(2, -3)$ to the straight line $4x - 3y + 8 = 0$ meets it at $M(a, b)$ and $a^3 - b^3 = k^3$,then $k=$

Find the equation of the right bisector of the line segment joining the points $(3, 4)$ and $(-1, 2).$

Vedclass Test Series

Exam Paper Generator

Online Exam Module