Question

A line intersects the $y$-axis and $x$-axis at the points $P$ and $Q$ respectively. If $(2,5)$ is the mid-point of $PQ$, then the coordinates of $P$ and $Q$ are respectively

• A. $(0,5)$ and $(2,0)$
• B. $(0,8)$ and $(4,0)$
• C. $(0,4)$ and $(10,0)$
• D. $(0,10)$ and $(4,0)$

Answer 1

Answer: (C)

$(0,4)$ and $(10,0)$

$GiventhatthepointR(p,q)=(2,5)isthemidpointofthelinesegmentPQjoiningthepointsP=(x_1,y_1)=(0,y)andQ=(x_2,y_2)=(x,0).\therefore bymid-pointformulawehavep=\frac{x_1+x_2}{2}andq=\frac{y_1+y_2}{2}.⟹p=\frac{0+x}{2}=\frac{x}{2}andq=\frac{y+0}{2}=\frac{y}{2}⟹\frac{x}{2}=2i.ex=4and\frac{y}{2}=5i.ey=10\therefore ThecoordinatesofPis(0,y)=(0,10)andthecoordinatesofQis(x,0)=(4,0)Ans-OptionD$