Question

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nswer the questions based on above:
(1) If A(2, 3), B((4, 6), C(7, 4) and D(a, b) are the vertices of a quadrilateral, such that diagonals A
and BD intersects each other at O. If O is mid point of AC and BD then find the value of 4 and
(ii) Three vertices of a parallelogram taken in order are (0, 3), (0, 0) and (5, 0), then find the fourt
, vertex.
i) If P(5. 2), Q(2,-2) and R(2, y) are vertices of a right-angled triangle where ZQ = 90° then find

Answer 1

The detailed answer explains how to find the missing vertex of a quadrilateral, the fourth vertex of a parallelogram, and the value of a coordinate in a right-angled triangle.

Step-by-step explanation:

In the given question, we are given that quadrilateral ABCD has vertices A(2, 3), B(4, 6), C(7, 4), and O is the midpoint of AC and BD. Since O is the midpoint of AC, we can find the coordinates of O by averaging the x-coordinates and y-coordinates of A and C, respectively. Similarly, we can find the coordinates of D by averaging the x-coordinates and y-coordinates of B and O, respectively. Once we have the coordinates of D, we can find the values of a and b.

For the second part of the question, we are given three vertices of a parallelogram: A(0, 3), B(0, 0), and C(5, 0). To find the fourth vertex, D, we can use the property that opposite sides of a parallelogram are parallel. Using this property, we can determine the distance and direction between A and B, and then use it to find the coordinates of D.

Lastly, for the right-angled triangle with vertices P(5, 2), Q(2, -2), and R(2, y), we know that angle ZQ is 90°. Since angle ZQ is a right angle, we can use the Pythagorean theorem to find the length of QR. By knowing the length of QR and the coordinates of Q, we can find the value of y by using the slope formula.

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