Answer:
The midpoint of the segment is (-0.5,0.5).
Step-by-step explanation:
Midpoint of a segment:
The midpoint of a segment is given by the mean of its coordinates.
Segment with end points (4,2),(-5,-1)
x-coordinates: 4 and -5
y-coordinates: 2 and -1
x-coordinate of the midpoint:
y-coordinate of the midpoint:
The midpoint of the segment is (-0.5,0.5).
Given:
x, y and z are integers.
To prove:
If is even, then at least one of x, y or z is even.
Solution:
We know that,
Product of two odd integers is always odd. ...(i)
Difference of two odd integers is always even. ...(ii)
Sum of an even integer and an odd integer is odd. ...(iii)
Let as assume x, y and z all are odd, then is even.
is always odd. [Using (i)]
is always odd. [Using (i)]
is always even. [Using (ii)]
is always odd. [Using (iii)]
is always odd.
So, out assumption is incorrect.
Thus, at least one of x, y or z is even.
Hence proved.