Answer:
The mid-point (p + q , q + p) of AB is the same distance from the x-axis and the y-axis
Step-by-step explanation:
*<em> Lets explain how to solve the problem</em>
- Any point will be equidistant from the x-axis and the y-axis must have
equal coordinates
- Ex: point (4 , 4) is the same distance from the x-axis and the y-axis
because the distance from the x-axis to the point is 4 (y-coordinate)
and the distance from the y-axis and the point is 4 (x-coordinate)
- If (x , y) is the mid-point of a segment its endpoints are
and 
, then
and 
* <em>Lets solve the problem</em>
∵ Point A has coordinates (p , q)
∵ Point B has coordinates (p + 2q , q + 2p)
- The mid-point of AB is (x , y)
∵ 
∴ 
- Take 2 as a common factor from the terms of the numerator
∴ 
- Divide up and down by 2
∴ x = p + q
∵ 
∴ 
- Take 2 as a common factor from the terms of the numerator
∴ 
- Divide up and down by 2
∴ y = q + p
∴ <em>The mid point of AB is (p + q , q + p)</em>
- p + q is the same with q + p
∵ The x-coordinate of the mid point of AB is p + q
∵ The y-coordinate of the mid point of AB is q + p
∵ p + q = q + p
∴ The coordinates of the mid-point of AB are equal
- According the explanation above
∴ The mid-point (p + q , q + p) of AB is the same distance from the
x-axis and the y-axis
