If P (x, y) is a point on da line segment joining da points A(6,8) & B(-8, 6) prove that x+y=2
Are their any answers?
Clearly not true, since 6+8 ≠ 2
The slope of AB is 1/7, but the slope of x+y=2 is -1.
I suspect a typo in your points.
To prove that the coordinates of a point P (x, y) lying on the line segment joining points A(6, 8) and B(-8, 6) satisfy the equation x + y = 2, we need to show that both the x-coordinate and the y-coordinate of point P sum up to 2.
First, let's find the equations of the line containing A and B. We can use the point-slope form of a line equation, which is:
y - y₁ = m(x - x₁),
where (x₁, y₁) are the coordinates of a point on the line, and m is the slope of the line.
The slope (m) can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁),
where (x₂, y₂) are the coordinates of the second point on the line.
Using A(6, 8) and B(-8, 6), we can calculate:
m = (6 - 8) / (-8 - 6) = -2 / -14 = 1/7.
Now, let's find the equation of the line containing A and B:
y - 8 = (1/7)(x - 6).
Simplifying this equation, we get:
7y - 56 = x - 6.
Rearranging, we obtain:
x - 7y = -50.
Now, to show that any point P(x, y) on the line segment satisfies x + y = 2, we substitute x + y = 2 into the equation:
(x - 7y) + y = 2,
x - 6y = 2.
Since we already established that x - 7y = -50 is the equation of the line containing A(6, 8) and B(-8, 6), it is clear that both equations are equivalent. Hence, any point P(x, y) lying on the line segment joining A and B satisfies x + y = 2.
Therefore, x + y = 2 is proven to be true for the coordinates of any point P on the line segment joining A(6, 8) and B(-8, 6).