The midpoint of a point A(5,x) and B(y,2)is(2,2)find the value of x and y

Using the x-coordinates of A, B, and the midpoint:

$$\frac{5 + y}{2} = 2$$

Multiply both sides by 2:

$$5 + y = 2 \times 2$$ $$5 + y = 4$$

Subtract 5 from both sides:

$$y = 4 - 5$$ $$y = -1$$

Using the y-coordinates of A, B, and the midpoint:

$$\frac{x + 2}{2} = 2$$

Multiply both sides by 2:

$$x + 2 = 2 \times 2$$ $$x + 2 = 4$$

Subtract 2 from both sides:

$$x = 4 - 2$$ $$x = 2$$

The values are $x = 2$ and $y = -1$.

$$\boxed{x=2, y=-1}$$

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