Question

Points M and N are two of the vertices of a right triangle. They are the endpoints of the hypotenuse bar (MN) of the triangle. The third vertex lies in the fourth quadrant. Plot a point at the location of the third vertex.

Answer 1

The third vertex of a right triangle in the fourth quadrant with MN as the hypotenuse must be plotted below the point on the x-axis or to the right of the point on the y-axis, as per the Pythagorean theorem.

Step-by-step explanation:

When plotting the third vertex of a right triangle in the fourth quadrant with MN as the hypotenuse, it's essential to remember that this will involve plotting a point that must lie either directly vertical or horizontal from one of the endpoints of the hypotenuse, as these will represent the two legs of the triangle. The fourth quadrant is where both x and y coordinates are positive. So, if we consider point M or N to be touching the x-axis, then the third point must be vertically below it to ensure it lies within the fourth quadrant. If we consider point M or N to be touching the y-axis, then the third point must be horizontally to the right. This is because the sides of the triangle represented by the x and y axes should be perpendicular to each other, as indicated by the Pythagorean theorem a² + b² = c². Hence, the vertex should be plotted either below the point that lies on the x-axis or to the right of the point that lies on the y-axis within the fourth quadrant.