Mei is writing a coordinate proof involving a right isosceles triangle. Mei places her triangle on the coordinate plane such that one of the legs of the triangle lies along the x-axis and the other leg is parallel to the y-axis.
~ What coordinates should she assign to this third vertex of the right isosceles triangle?

Answer: (a,a)

Step-by-step explanation:

Given: A  right isosceles triangle which is placed on the coordinate plane such that one of the legs of the triangle lies along the x-axis and the other leg is parallel to the y-axis.

From the given figure one vertex is on origin(0,0) and second on x -axis as (a,0) .ii.e. one side of the triangle is on the x axis with length 'a' and the side parallel to the y axis should perpendicular to the x axis with length 'a'.(∵ two sides are equal in a right isosceles triangle)

So the coordinates should she assign to the third vertex of the right isosceles triangle is (a,a).[as the point lie above the point (a,0), so its x abscissa should be same]

The third vertex of a right isosceles triangle where one leg lies on the x-axis and the second leg is parallel to the y-axis would have equal x and y coordinates, assuming the second vertex is at (a,0). Therefore, the third vertex would be at (a,a), for any real numerical value of 'a'. This makes use of key concepts in coordinate geometry.

In the context of mathematics, specifically coordinate geometry, Mei can assign the third vertex of this right isosceles triangle to any point that is equally distant from both the x and y axes. Assuming the other two vertices of the triangle are at the origin (0,0) and on the x-axis (a,0), then the coordinates of the third vertex would be (a,a).

Right isosceles triangle is a special type of triangle where two sides are equal in length and the angle between them is 90 degrees. Since the legs of the triangle are along the x and y axes, this leads to the third vertex being on the line y=x.

A coordinate proof involves using the properties and definition of the geometric figures in the coordinate plane. It involves calculations with the coordinates of the vertices of the figures. In the case of coordinate geometry, it's essential to understand the placement of points on the x-y plane.

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