Question

12. Three vertices of a parallelogram ABCD are A(1,4), B(-2, 3) and C(5,8). The ordinate of the fourth vertex D is (a) 8 (b) 9 (c) (d) 6 ​

Answer 1

Answer:

b option which is 9

Explanation:

B is the correct correct option which is 9

Answer 2

The ordinate of the fourth vertex D is 9  if ABCD is a parallelogram with vertex  A(1,4), B(-2, 3) and C(5,8).

Given:

• A parallelogram ABCD
• Three Vertices:
• A (1 , 4)
• B (-2 ,3 )
• C (5 , 8)

To Find:

• The ordinate of the fourth vertex D
• (a) 8
• (b) 9
• (c)
• (d) 6 ​

Solution:

Concept to be used:

Diagonals of a parallelogram bisect each other

Ordinate of  a point is y coordinate of that point

Mid point of (a , b) and ( c , d)  can be calculated as

(a + c)/2 , (b + d)/2

Step 1:

Find y coordinate of mid point of diagonal AC  

(4 + 8)/2  = 6

Step 2:

Assume y coordinate of D as k and Find y coordinate of mid point of diagonal  BD and Equate with y coordinate of mid point of diagonal AC and solve for k

(3 + k)/2  = 6

=> 3 + k = 12

=> k = 9

The ordinate of the fourth vertex D is  9

Correct option is b) 9

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