Question

The midpoint of segment TS is the origin. Point T is located in Quadrant 2. what quadrant contains point S. Explain.

Answer 1

The fourth. If the midpoint of TS is the origin and Point T is located in quadrant 2, then point S must be located opposite from point T which is in the fourth quadrant

Answer 2

The quadrant in which point S lie is:

Quadrant 4.

since, the x-coordinate is positive and y-coordinate is negative

Explanation:

We know that if the point C(c,d) lies in between A(a,b) and B(a',b') then the coordinates of the point C is given by:

`c=(a+a')/(2)\ ,\ d=(b+b')/(2)`

Here the midpoint of segment TS is the origin i.e. (c,d)=(0,0)

A=T and B=S

Also, Point T is located in Quadrant 2.

i.e. a<0 and b>0

We have:

`0=(a+a')/(2)\ ,\ 0=(b+b')/(2)\\\\a+a'=0\ ,\ b+b'=0\\\\a'=-a\ ,\ b'=-b`

Hence, we have:

`a'>0\ ,\ b'<0`

This means that point S lie in quadrant 4