Home › Kerala SSLC (Class 10) › Mathematics › Coordinate Geometry › The fourth vertex of a parallelogram with three …
The fourth vertex of a parallelogram with three given vertices (1, 3), (5, 4), (2, 5) is (taking the missing vertex opposite (1, 3)):
A(6, 4)
B(8, 12)
C(6, 6)
D(3, 7)
Answer & Solution
Correct answer: C. (6, 6)
1. In any parallelogram, the diagonals bisect each other.
2. So midpoint of diagonal joining (1, 3) and (x, y) = midpoint of diagonal joining (5, 4) and (2, 5).
3. Midpoint of the second diagonal = ((5+2)/2, (4+5)/2) = (3.5, 4.5).
4. So (1 + x)/2 = 3.5 → x = 6; and (3 + y)/2 = 4.5 → y = 6.
5. The fourth vertex is therefore (6, 6).
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
Related questions
The points (1, 5), (2, 3) and (minus 2, minus 11) are examined to check whether they are:If three points give an area of zero, what does that show?When the area formula gives a negative value for a triangle, you should:The area of the triangle with vertices (5, 2), (4, 7) and (7, minus 4) is:The area of the triangle with vertices (1, minus 1), (minus 4, 6) and (minus 3, minus 5) iBecause of that, the midpoint of the join of two points is found by:A midpoint divides a line segment in which ratio?The point dividing the join of (4, minus 3) and (8, 5) in the ratio 3 to 1 is: