Question:
If \((2,8)\) is one vertex and \(x-y+3=0\) is one diagonal of a square, then the equation of the other diagonal is
If \((2,8)\) is one vertex and \(x-y+3=0\) is one diagonal of a square, then the equation of the other diagonal is
Show Hint
The vertex does not lie on the given diagonal, so the other diagonal passes through it and is perpendicular to the first.
Updated On: Nov 12, 2026
- \(x+y-10=0\)
- \(x+y+10=0\)
- \(x-y+10=0\)
- \(x-y-10=0\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
The diagonals of a square are perpendicular to each other and bisect each other.
Step 2: Check the vertex
Put \((2,8)\) in \(x-y+3\): \(2-8+3=-3\ne 0\). So the vertex is not on the given diagonal and must lie on the other diagonal.
Step 3: Slope
The given diagonal has slope \(1\), so the other diagonal has slope \(-1\).
Step 4: Equation
\(y-8=-1(x-2)\Rightarrow x+y-10=0\)
Final Answer:
The other diagonal is x + y - 10 = 0. \[ \boxed{\text{(A) }x+y-10=0} \]
The diagonals of a square are perpendicular to each other and bisect each other.
Step 2: Check the vertex
Put \((2,8)\) in \(x-y+3\): \(2-8+3=-3\ne 0\). So the vertex is not on the given diagonal and must lie on the other diagonal.
Step 3: Slope
The given diagonal has slope \(1\), so the other diagonal has slope \(-1\).
Step 4: Equation
\(y-8=-1(x-2)\Rightarrow x+y-10=0\)
Final Answer:
The other diagonal is x + y - 10 = 0. \[ \boxed{\text{(A) }x+y-10=0} \]
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Straight lines Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The joint equation of lines passing through the origin and trisecting the first quadrant is ________
- Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is
- If , then and is:
- A circle with center is tangent to the -axis in the standard coordinate plane. What is the radius of this circle?
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions