Question

Fill in the blank:
The midpoint of the line segment joining the points (-1,2) and (3,4 ) lies in ........ quadrant.

Answer 1

SOLUTION

TO FILL IN THE BLANK

The midpoint of the line segment joining the points (-1,2) and (3,4 ) lies in _____ quadrant.

CONCEPT TO BE IMPLEMENTED

1. For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$

The midpoint of the line AB is

$\displaystyle \sf{ \bigg( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} \bigg)}$

2. We know that in two dimensional geometry the Cartesian plane is divided by coordinate axis in 4 quadrant

1. Quadrant I : Both the x - coordinates and y - coordinates are positive

2. Quadrant II : The x - coordinate is negative and the y - coordinate is positive

3. Quadrant III : Both the x - coordinates and y - coordinates are negative

4. Quadrant IV : The x - coordinate is positive and the y - coordinate is negative

EVALUATION

Here the given points are (-1,2) and (3,4 )

So the midpoint of the line segment joining the points (-1,2) and (3,4 )

$\displaystyle \sf{ = \bigg( \frac{ - 1 + 3}{2} , \frac{2 + 4}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{ 2}{2} , \frac{6}{2} \bigg)}$

$\displaystyle \sf{ = (1 , 3)}$

For the point (1,3)

x - coordinate = 1

y - coordinates = 3

Thus Both the x - coordinates and y - coordinates are positive

Hence the point lies in first quadrant

FINAL ANSWER

The midpoint of the line segment joining the points (-1,2) and (3,4 ) lies in first quadrant.

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