Square JKLM has vertices J(6,2),
K(z,2), L(-1,-5), and M(x,y).
What is x - y ?
6-(-5) = 11
To find the value of x - y, we first need to determine the coordinates of point M.
We know that square JKLM is a square, which means that all four sides are congruent (i.e., equal in length) and all four angles are right angles. Since sides JK and LM are parallel to the y-axis and sides KL and JM are parallel to the x-axis, we can determine the x and y coordinates of specific points.
From the information given, we know the coordinates of points J(6,2) and L(-1,-5). Using these points, we can find the length of the sides of the square.
The length of side JK is the difference between the x-coordinates of points J and K: JK = 6 - z.
The length of side LM is the difference between the x-coordinates of points L and M: LM = -1 - x.
Since JK is equal to LM (due to the square being congruent on all sides), we can equate the two expressions and solve for x:
6 - z = -1 - x.
Re-arranging this equation, we get:
x - z = 7.
Now, to find x - y, we need to determine the y-coordinate of point M. Since side JK is parallel to the y-axis, the y-coordinate of point M is the same as the y-coordinate of point K.
From the information given, we know that point K has a y-coordinate equal to 2. Therefore, the y-coordinate of point M is also 2.
Now we can substitute the values of x = 7 + z and y = 2 into x - y:
x - y = (7 + z) - 2 = 5 + z.
So, the value of x - y is 5 + z.