The vertices of a rectangle are
Q(−1,1), R(5,1), S(5,−3), and T(−1,−3). What is the point where the diagonals intersect?
To find the point where the diagonals of a rectangle intersect, we can find the midpoints of the diagonals.
The midpoint of the diagonal connecting vertices Q and S is the average of their x-coordinates and the average of their y-coordinates.
The x-coordinate of the midpoint = (x-coordinate of Q + x-coordinate of S) / 2.
= (-1 + 5) / 2
= 4 / 2
= 2.
The y-coordinate of the midpoint = (y-coordinate of Q + y-coordinate of S) / 2.
= (1 - 3) / 2
= -2 / 2
= -1.
Therefore, the midpoint of the diagonal QS is M(2, -1).
Similarly, the midpoint of the diagonal connecting vertices R and T is the average of their x-coordinates and the average of their y-coordinates.
The x-coordinate of the midpoint = (x-coordinate of R + x-coordinate of T) / 2.
= (5 - 1) / 2
= 4 / 2
= 2.
The y-coordinate of the midpoint = (y-coordinate of R + y-coordinate of T) / 2.
= (1 - 3) / 2
= -2 / 2
= -1.
Therefore, the midpoint of the diagonal RT is also M(2, -1).
Since both diagonals intersect at the same point M(2, -1), the point where the diagonals intersect is M(2, -1).
To find the point where the diagonals of a rectangle intersect, we can use the midpoint formula.
The diagonals of a rectangle bisect each other, meaning they intersect at their midpoints.
First, let's find the midpoint of segment QR.
The midpoint formula states that the coordinates of the midpoint M of a segment with endpoints (x₁, y₁) and (x₂, y₂) are given by:
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
For segment QR, the coordinates of Q are (-1, 1) and the coordinates of R are (5, 1).
Using the midpoint formula, we can find the midpoint of segment QR:
M₁ = ((-1 + 5) / 2, (1 + 1) / 2) = (2, 1)
Now, let's find the midpoint of segment ST.
The coordinates of S are (5, -3) and the coordinates of T are (-1, -3).
Using the midpoint formula, we can find the midpoint of segment ST:
M₂ = ((5 + (-1)) / 2, (-3 + (-3)) / 2) = (2, -3)
Since the diagonals of a rectangle bisect each other, the point of intersection is the same as the midpoints of both diagonals.
Thus, the point where the diagonals intersect is (2, 1).
the diagonals bisect each other. So that will be
the midpoint of QS
or
the midpoint of RT
I assume you know how to find the midpoint of a line segment.