MHT CET · Maths · Straight Lines
The diagonals of a parallelogram ABCD are along the lines \(x+3 y=4\) and \(6 x-2 y=7\). Then ABCD must be a
- A rectangle.
- B square.
- C rhombus.
- D cyclic quadrilateral
Answer & Solution
Correct Answer
(C) rhombus.
Step-by-step Solution
Detailed explanation
Slope of \(x+3 y=4\) is \(\mathrm{m}_1=-\frac{1}{3}\)
Slope of \(6 x-2 y=7\) is \(m_2=3\)
Here, \(\mathrm{m}_1 \cdot \mathrm{~m}_2=-1\)
\(\therefore \quad\) The diagonals are perpendicular to each other.
\(\therefore \quad\) Parallelogram ABCD is a rhombus.
Slope of \(6 x-2 y=7\) is \(m_2=3\)
Here, \(\mathrm{m}_1 \cdot \mathrm{~m}_2=-1\)
\(\therefore \quad\) The diagonals are perpendicular to each other.
\(\therefore \quad\) Parallelogram ABCD is a rhombus.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The first derivative of the function \(\left(\cos ^{-1}\left(\sin \sqrt{\frac{1+x}{2}}\right)+x^x\right)\) with respect to \(x\) at \(x=1\) isMHT CET 2025 Medium
- MHT CET 2016 Easy
- The equation \(x^3+x-1=0\) hasMHT CET 2023 Easy
- If \((\mathrm{a}+\mathrm{b} x) \mathrm{e}^{\frac{\mathrm{y}}{x}}=x\), then \(x^3 \frac{\mathrm{~d}^2 \mathrm{y}}{\mathrm{d} x^2}\) is equal toMHT CET 2025 Hard
- The value of \(\frac{{ }^{10} \mathrm{C}_{\mathrm{r}}}{{ }^{11} \mathrm{C}_{\mathrm{r}}}\), when both the numerator and denominator are at their greatest values, isMHT CET 2023 Medium
- The value of \(x\) such that the matrix \(\left[\begin{array}{lll}x & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 3 & 5\end{array}\right]\) is not invertible isMHT CET 2020 Easy
More PYQs from MHT CET
- Which of the following combination of 7 identical capacitors each of \(2 \mu \mathrm{F}\) gives a capacitance of \(\frac{10}{11} \mu \mathrm{F}\) ?MHT CET 2023 Medium
- A rectifier is used toMHT CET 2021 Easy
- Three discs \(x, y\) and \(z\) having radii \(2 \mathrm{~m}, 2 \mathrm{~m}\) and \(6 \mathrm{~m}\) respectively are coated on outer surfaces. The wavelength corresponding to maximum are power radiated by them respectively thenMHT CET 2022 Hard
- Which from following monomers is used to obtain polymer represented asMHT CET 2024 Medium
- If \(\sin (x+y)+\cos (x+y)=\sin \left[\cos ^{-1}\left(\frac{1}{3}\right)\right]\), then \(\frac{d y}{d x}=\)MHT CET 2020 Medium
- In an experiment four quantities \(p, q, r\) and \(s\) are measured with percentage \(3 \%, 2 \%, 3 \%\) and \(1 \%\) respectively. Quantity ' A ' is calculated as follows \(\mathrm{A}=\frac{\mathrm{pq}^2}{\mathrm{r}^2 \mathrm{~s}^4}\), the percentage error in ' A ' isMHT CET 2025 Easy