Question

Which expressions can be used to find the coordinates of the midpoint of PQ with endpoints P(3, –1) and Q(–7, –6)? Select THREE options.

Answer 1

A line segment is a straight line with finite length, and thus, have to endpoints(points on either end). The correct options are 2, 3, and 5.

What are the coordinates of the midpoint of the line segment AB?

A line segment is a straight line with finite length, and thus, have to endpoints(points on either end).

Suppose we've two endpoints of a line segment as A(p,q), and B(m,n), Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

$x = \dfrac{p+m}{2}$

and

$y = \dfrac{q+n}{2}$

The midpoint of the points P(3, –1) and Q(–7, –6) is,

x = (-7+3)/2 = -4/2 = -2

y = (-6-1)/2 = -7/2 = -3.5

Now, if we look at the options, the third option will give as the value of the x-coordinate as,

[(1/2)(-7-3)] + 3

= [(1/2)(-10)] + 3

= -5 + 3

= -2

This is the actual coordinate of the midpoint, therefore, this option is correct.

Similarly, the option two expresses the y-coordinate of the midpoint,

(-1 - 6)/2 = -3.5

Also, option five correctly depicts the value of y-coordinate,

-(5/2)-1 = -2.5 - 1 = -3.5

Hence, the correct options are 2, 3, and 5.

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