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Fill in the blank.

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

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Detailed Solution

The mid-point of the line segment joining the points (-1,2) and (3,4) lies in 1st quadrant.
Given points,
(-1,2) and (3,4).
Let, coordinate of midpoint of (-1,2) and (3,4) is

(x, y)

.
Since, if the coordinates of two points are

x 1, y 1

and

x 2, y 2

then the coordinate of the middle point of the two points will be

x 1 + x 2 2, y 1 + y 2 2

.
Then,
Coordinates of midpoint of (-1,2) and (3,4) is

(x, y) = x 1 + x 2 2, y 1 + y 2 2 ⇒ (x, y) = − 1 + 3 2, 2 + 4 2 ⇒ (x, y) = 22, 62 ⇒ (x, y) = (1, 3)

Since both

x and y

are positive, therefore

(x, y)

1st quadrant.
Hence, answer is 1st quadrant.

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