How many possible points so that the x-coordinate an the y-coordinate are additive inverses of each other, and the differnce of the coordinates is 10.
ABS(X-Y)=10
PICK A FEW POINTS.
y=1000, THEN X=1010 OR 990
X=-37.3 THEN Y= -27.3 OR -47.3
Looks like I could pick millions, or an infinite number, of points
I can see only
(5,-5) and (-5,5)
any other pairs of additive inverses do not differ by 10
To find the possible points where the x-coordinate and the y-coordinate are additive inverses of each other, we need to define a system of equations based on the given conditions.
Let's assume the x-coordinate is represented by 'x' and the y-coordinate is represented by 'y'. We have two conditions:
1. The x-coordinate and the y-coordinate are additive inverses:
This can be expressed as x = -y.
2. The difference between the coordinates is 10:
This can be expressed as x - y = 10.
Now, we can solve this system of equations to find the values of x and y.
We substitute the value of x in the second equation with -y from the first equation:
(-y) - y = 10
Simplifying, we get:
-2y = 10
Dividing by -2, we find:
y = -5
Now, substituting this value back into the first equation (x = -y), we get:
x = -(-5) = 5
Therefore, the possible point where the x-coordinate and the y-coordinate are additive inverses of each other, and the difference of the coordinates is 10, is (5, -5).