Question

Please help !!!!!!!!!!!!

A line segment has one end point at (a,0) and its other endpoint on the line yx. If the midpoint of this line segment is (2019,2020). What is the value of a?

Answer 1

a=-2

Explanation:

If a line segment has one endpoint on the line y=x, then its coordinates are (b,b). The first endpoint of the segment is at point (a,0). We can find the coordinates of the midpoint of this segment as the average value:

`x_{\text{midpoint}}=\frac{x_{\text{first endpoint}}+x_{\text{second endpoint}}}{2},\\ \\y_{\text{midpoint}}=\frac{y_{\text{first endpoint}}+y_{\text{second endpoint}}}{2}.`

Thus,

`2019=(a+b)/(2),\\ \\2020=(0+b)/(2).`

From the second equation

`b=2\cdot 2020=4040.`

Substitute it into the first equation:

`a+4040=2\cdot 2019,\\ \\a=4038-4040=-2.`