# How to find a point on the line? x cordinate is given as x.

The diagram is like a rectangle is inscribed in an isosceles right triangle whose hypotneus is 2 units long. AB is another side of the right triangle and P is a point on it(also a vertex of the rectangle). How do I find the cordinates of P(x,?)
A hint is given that I have to write equation of the line AB.

## To find the y-coordinate of point P (x, ?) on the line AB, we need to first write the equation of the line AB using the given information.

Let's analyze the given information:

- We have an isosceles right triangle, meaning one of its angles is 90 degrees, and the other two angles are congruent.

- The hypotenuse of the triangle is 2 units long.

- Point P is a vertex of the rectangle inscribed in the triangle and lies on side AB.

To find the equation of line AB, we need to determine the slope and one point on the line.

The slope of line AB can be found using the fact that the opposite angles in an isosceles right triangle are congruent. Since line AB is perpendicular to the hypotenuse, we can determine the slope by considering the opposite sides.

Since one of the sides AB is horizontal, we can say that its slope is 0.

Therefore, the equation of line AB can be written as y = 0x + b, where b is the y-intercept.

To find the value of b, we need to find a point on line AB.

Looking at the diagram, we can see that point A is the intersecting point of the hypotenuse and the horizontal side. So, it has coordinates (2, 0).

Substituting these coordinates into the equation of line AB, we get:

0 = 0(2) + b
0 = 0 + b
b = 0

Now we have the equation of line AB as y = 0x + 0, which simplifies to y = 0.

Since we want to find the y-coordinate of point P, we can substitute the given x-coordinate (x) into the equation:

y = 0(x) + 0
y = 0

Therefore, the y-coordinate of point P (x, ?) on line AB is 0.

In summary, the coordinates of point P are (x, 0).