Maths · Straight line: Various forms of equations of a line, intersection of lines, angles between two lines
The diagonals of a parallelogram are along the lines and then must be
The diagonals of a parallelogram \( P Q R S \) are along the lines \( x+3 y=4 \) and \( 6 x-2 y=7, \) then \( P Q R S \) must be \( a \)
- A. rectangle
- B. square
- C. cyclic quadrialtaral
- D. rhombus
Step-by-step solution
The diagonals are along lines x+3y=4 (slope -1/3) and 6x-2y=7 (slope 3). Their product is -1, so the diagonals are perpendicular. In a parallelogram, perpendicular diagonals imply it is a rhombus. Hence, PQRS must be a rhombus.
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