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  • 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, 10) and (– 4, 0) (C) (0, 4) and (– 10, 0) (D) (0, – 10) and (4,

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, 10) and (– 4, 0)

(C) (0, 4) and (– 10, 0)

(D) (0, – 10) and (4, 0)

Answers (1)

Point

 P=(0, y)\{ at\ y -axis x=0\}
\\\mathrm{Q}=(\mathrm{x}, 0) \quad\{ at \mathrm{x} axis \mathrm{y}=0\} \\\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=(0, \mathrm{y}) \quad\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=(\mathrm{x}, 0)

Mid-point =(2,-5)

\\\left[\left(\frac{\mathrm{x}_{1}+\mathrm{x}_{2}}{2}\right),\left(\frac{\mathrm{y}_{1}+\mathrm{y}_{2}}{2}\right)\right]=(2,-5)\\\left(\frac{0+x}{2}, \frac{y+0}{2}\right)=2,-5 \\\frac{x}{2}=2 \quad \frac{y}{2}=-5

\\ x=4 \: \: \: \: \: \: \: \: y=-10 \\ \text { Point } P(0,-10), \ and\ Q(4,0)

Hence, option D is correct.

Posted by

infoexpert21

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