What are the coordinates of vertex D?
Direction: Consider the following for the two (02) items that follow :<br>ABCD is an isosceles trapezium and AB is parallel to DC. Let A(2,3), B(4,3), C(5,1) be the vertices.
- A. (2, 1)
- B. (1, 2)
- C. (1, 1) ✓
- D. (3, 1)
Correct Answer: C. (1, 1)
Explanation
Since A(2,3) and B(4,3) have the same y-coordinate, the line AB is horizontal (y=3). Since DC is parallel to AB, DC is also horizontal, meaning the y-coordinate of D is the same as C, which is 1. For an isosceles trapezium with horizontal bases, the line of symmetry is vertical and passes through the midpoints of both bases. The x-coordinate of the midpoint of AB is (2+4)/2 = 3. Setting the x-coordinate of the midpoint of DC to 3 gives (x_D + 5)/2 = 3, leading to x_D = 1. Thus, D is (1,1).
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