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in Three-dimensional geometry by (52.5k points)

The sides of a rhombus ABCD are parallel to the lines, x – y + 2 = 0 and 7x – y + 3 = 0. If the diagonals of the rhombus intersect at P(1, 2) and the vertex A (different from the origin) is on the y-axis, then the ordinate of A is 

(A) 5/2 

(B) 7/4 

(C) 2 

(D) 7/2

1 Answer

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Best answer

Answer is (A) 5/2

From the given data, we plot the graph as shown in the following figure:

Now, the midpoint of AC is

(a + 0)/2 = 1 ⇒ a = 2

(b + α)/2 = 2 ⇒ b + α = 4

The sides of a rhombus ABCD are parallel to the lines x – y + 2 = 0 and 7x – y + 3 = 0.

Equation of parallel diagonals is

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