The following question appeared 2009 Grade 12 Advance Mathematics Examination Paper.
Program
A (4, 2), B (4, 5) C (1, 5) and D (1, 2) are vertices of a quadrilateral . Show that AC and BD have the same mid point.
Questions.
i). Show that AC and BD have the same mid point. (2 marks)
ii). Show that the diagonals AC and BD are
perpendicular to each other. (3 marks)
iii). Show that the diagonals have equal lengths. (2 marks)
Solutions 1.
i). To show that the diagonals AC and BD of the quadrilateral ABCD have the same midpoint, you can calculate the midpoints of both diagonals and demonstrate their equality.
The midpoint of a line segment between two points ( is given by the coordinates:
Solution 2
To show that the diagonals AC and BD of the quadrilateral are perpendicular, we need to demonstrate that the product of the slopes of AC and BD is -1, as two lines are perpendicular if and only if the product of their slopes is -1.
Show that the diagonals have equal lengths
to find the length of BD, we use the distance formula:
The length of a line segment between two points (x1, y1) and (x2, y2) is given by the distance formula
By Substitution
Also watch video explanation below
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