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

Answer:

The quadrant in which point S lie is:

                     Quadrant 4.

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

Step-by-step 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:

$c=\dfrac{a+a'}{2}\ ,\ d=\dfrac{b+b'}{2}$

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:

$0=\dfrac{a+a'}{2}\ ,\ 0=\dfrac{b+b'}{2}\\\\a+a'=0\ ,\ b+b'=0\\\\a'=-a\ ,\ b'=-b$

Hence, we have:

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

This means that point S lie in quadrant 4