If the points A(-2, -1), B(1, 0), C(p, 3) and D(1, q) form a parallelogram ABCD, find the values of p and q.

A(-2, -1), B(1, 0), C(p, 3) and D(1, q) are the vertices of a parallelogram ABCD as shown in the figure below: ∴ Diagonal AC and BD bisect each other at O. O is the mid-point of AC as well as BD. Let the coordinates of O be (x, y). When O is the mid-point of AC, then by mid-point formula When O is the mid-point of BD, then by mid-point formula Now comparing, we get the values of the coordinates of point O in both cases, Hence, the value of p = 4 and q = 2.

Calculate the length of the median through the vertex A of the triangle ABC with vertices A(7, -3), B(5, 3) and C(3, -1).

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Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid-point of one side is (0, 3).

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Mathematics

If the points A(-2, -1), B(1, 0), C(p, 3) and D(1, q) form a parallelogram ABCD, find the values of p and q.

Section Formula

Related Questions

Calculate the length of the median through the vertex A of the triangle ABC with vertices A(7, -3), B(5, 3) and C(3, -1).

Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid-point of one side is (0, 3).

If two vertices of a parallelogram are (3, 2), (-1, 0) and its diagonals meet at (2, -5), find the other two vertices of the parallelogram.

Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0) and C(4, 0). Find the fourth vertex D.