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).

Let A(-1, 4) and B(5, 2) be the two points and let C(x, y) be the third vertex of the triangle as shown in the figure below: By mid-point formula, mid-point of AB Since, (0, 3) is not the mid-point of AB hence, it is either the mid point of AC or BC. Let D(0, 3) be the midpoint of AC. So, by mid-point formula, ⇒ x - 1 = 0 and y + 4 = 6 ⇒ x = 1 and y = 2. ∴ Coordinates of C will be (1, 2). Let D(0, 3) be the midpoint of BC. So, by mid-point formula, ⇒ x + 5 = 0 and y + 2 = 6 ⇒ x = -5 and y = 4. ∴ Coordinates of C will be (-5, 4). Hence, the coordinates of C will be (1, 2) or (-5, 4).

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.

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Show by section formula that the points (3, -2), (5, 2) and (8, 8) are collinear.

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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.

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Mathematics

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).

Section Formula

Related Questions

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.

Show by section formula that the points (3, -2), (5, 2) and (8, 8) are collinear.

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.