To find the coordinates of the fourth corner of the square given the three corners \((1, 7)\), \((5, 3)\), and \((9, 7)\), we can start by identifying the relationship between the given points.
-
The points \((1, 7)\) and \((9, 7)\) share the same y-coordinate, which suggests that they are on a horizontal line. The distance between these points is \(9 - 1 = 8\).
-
The point \((5, 3)\) has a y-coordinate of \(3\) and forms a right angle with the line segment between \((1, 7)\) and \((9, 7)\).
-
We can find the coordinates of the fourth corner by determining the horizontal and vertical distances. Since \((5, 3)\) is below the line connecting \((1, 7)\) and \((9, 7)\) and forms a right angle with these points:
-
The fourth corner must also maintain the 8 units horizontal distance between \((1, 7)\) and \((9, 7)\) and also be at the same y-coordinate level as \((5, 3)\).
-
The fourth corner can be calculated by moving from \((5, 3)\) up to the same y-level as the other two corners, which is \(7\). Therefore:
- We need to find \(x\) such that the distance remains the same.
The coordinates for the fourth corner can be calculated using the parallels of the horizontal segments to maintain a square format. The possible calculations give us the horizontal alignment which will yield \((5, 7)\).
Thus, the coordinates of the fourth corner of the square are \((5, 7)\).
The correct answer is: • (5, 7)
1 answer