Determine the point with equal coordinates on the line y= 0.5x -0.5
We need to find the point with equal coordinates on the line y= 0.5x -0.5.
The point can be expressed as (m, m).
Now, as this lies on the line y= 0.5x -0.5 , we have
m = 0.5*m - 0.5
subtract 0.5*m from both the sides
=> 0.5m = -0.5
divide by 0.5
=> m = -1
The point has equal coordinates (-1,-1) and 0.5*-1 - 0.5 = -1
Therefore we have the point (-1,-1) on the line y= 0.5x -0.5.
We'll denote the point with that has equal coordinates as M(m,m).
Since the point is located on the line y = 0.5x - 0.5, it's coordinates verify the expression of the line.
We'll put y = f(x) and we'll substitute x and y by the coordinates of the given point:
f(m) = 0.5m - 0.5 (1)
But f(m) = m (2)
We'll conclude from (1) and (2) that:
0.5m - 0.5 = m
We'll isolate m to the left side.
0.5m - m = 0.5
-0.5m = 0.5
We'll divide by -0.5 both sides:
m = -1
The given line is y = 0.5x-0.5.
Since both x and y coordinates are equal and is a point on the line y = 0.5x-0.5, we assume that ( c , c ) is point.
Therefore (c,c) should satisfy y = 0.5x-0.5.
So we substitute y=c and x = c in y = 0.5x-0.5:
c = 0.5c -0.5.
c-0.5c = -0.5.
0.5c = -0.5.
Therefore c = -0.5/0.5 = -1.
Therefore (-1, -1) is a point on the line y = 0.5x-0.5