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  • 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 :Option: 1 <img alt="( 2,\; 2 )" src="https:

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 :

Option: 1

( 2,\; 2 )            


Option: 2

( 4,\; 5 )


Option: 3

( 3,\; 4 )


Option: 4

( 7,\; 7 )


Answers (1)

best_answer

\\\text{Slope of PQ}=\frac{5-3}{4-2}=1\\ \text{So slope of Line L}=-1\\ \text{Mid point of PQ is on the line L so }\\ M=(3,4)\\ \text{Equation of line L}\\ y-4=-1(x-3)\\ x+y=7\\\\ \begin{array}{l}{\text {Image of } P\left(x_{1}, y_{1}\right) \text { on the line } L: a x+b y+c=0 \text { is } Q\left(x_{2}, y_{2}\right) \text { , then }} \\ {\frac{x_{2}-x_{1}}{a}=\frac{y_{2}-y_{1}}{b}=-\frac{2\left(a x_{1}+b_{1}+c\right)}{\left(a^{2}+b^{2}\right)}}\end{array}\\ {\frac{x_{2}-0}{1}=\frac{y_{2}-0}{1}=-\frac{2\left(1 \cdot 0+1 \cdot 0-7\right)}{\left(1^{2}+1^{2}\right)}}\\ (x_2,y_2)=(7,7)

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