Question

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Answer 1

SOLUTION

GIVEN

A line intersects the x-axis and y-axis at the point P and Q respectively

(2,3) is the mid-point of PQ

TO DETERMINE

The coordinates of P and Q

EVALUATION

Here it is given that a line intersects the x-axis and y-axis at the point P and Q respectively

Let the coordinates of P is ( a, 0) & Q is (0,b)

Then the equation of the line PQ is

$\displaystyle \sf{ \frac{x}{a} + \frac{y}{b} = 1} \: \: \: .......(1)$

Now suppose that the midpoint of the line PQ is R

Then the coordinates of the point R is

$\displaystyle \sf{ = \bigg( \: \frac{a + 0}{2} \:, \: \frac{0 + b}{2} \: \bigg)}$

$= \displaystyle \sf{ \bigg( \: \frac{a}{2} \:, \: \frac{ b}{2} \: \bigg)}$

It is also stated that (2,3) is the mid-point of PQ

So by the given condition

$\displaystyle \sf{ \frac{a}{2} = 2 \: \: \: \: \: and \: \: \: \: \: \frac{ b}{2} = 3\: }$

$\displaystyle \sf{ \implies a = 4 \: \: \: \: \: and \: \: \: \: \: b = 6 }$

Hence the coordinates of P is ( 4,0) & Q is (0,6)

Graph : For graph refer to the attachment

FINAL ANSWER

The coordinates of P is ( 4,0) & Q is (0,6)

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