Final answer:
The fourth vertex of the square with the three given vertices (8,7), (4,7), and (4,3) is at point (8,3). This is determined by using the properties of a square and aligning the point horizontally to (4,3) and vertically to (8,7).
Step-by-step explanation:
To find the location of the fourth vertex of Diraj's square on the coordinate grid when given three vertices at points (8,7), (4,7), and (4,3), you must understand that the sides of a square are equal in length and the angles are all right angles (90 degrees). Considering that the given points form two sides of the square, we can deduce the location of the fourth vertex.
Firstly, observe that (8,7) and (4,7) share the same y-coordinate. This implies they are horizontally aligned, and thus form one side of the square. The horizontal distance between them is |8 - 4| = 4 units.
Secondly, the points (4,7) and (4,3) share the same x-coordinate, indicating they are vertically aligned and form another side of the square. The vertical distance between them is also 4 units, which is consistent with our square's properties.
Therefore, to find the fourth vertex, we must look for a point that is 4 units horizontally away from (4,3) and aligned with (8,7). The only point that satisfies these conditions is on the right side and below (8,7), which gives us the fourth vertex at (8,3).