Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2023MathematicsStraight Lines

The distance of the point (3,4) from the line 3 x+2 y+7=0 measured along the line parallel to y-2 x+7=0 is equal to

Options

  1. A24 5 7
  2. B3 5
  3. C23 5 7
  4. D4 5

Correct answer

A. 24 5 7

Step-by-step solution

The slope of the line, y-2 x+7=0 array ll y =2 x-7 Slope (m) =2 Slope of P Q =m_ P Q =2 Equation of P Q & array (y-4)=2(x-3) On putting, the value of y in Eq. (ii), we get aligned & & 3 x+2(2 x-2)+7 & =0 & & 7 x=-3 & x=- 3 7 aligned Then, y=2 (- 3 7 )-2=- 20 7 So, coordinates of Q= (- 3 7 , -20 7 ) Thus, distance P Q= (3- ( -3 7 )^2 )+ (4- (- 20 7 ) )^2 = 24 5 7

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are (1,2) and (4,5) , is 2025The coordinate axes are rotated about the origin in the counter clockwise direction through an angle 60^ . If a and b are the intercepts made on the new axes by a straight line who 2025The image of a point (2,-1) with respect to the line x-y+1=0 is 2025If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle 4 with the negative X -axis in the negative directi 2025A straight line passing through the origin O meets the parallel lines 4 x+2 y=9 and 2 x + y +6=0 at the points P and Q respectively. Then the point O divides the line segment PQ in 2025A (4,3), B (2,5) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoi 2025By shifting the origin to the point (2,3) through translation of axes, if the equation of the curve x^2+3 x y-2 y^2+4 x-y-20=0 is transformed to the form Ax ^2+ Bxy + Cy ^2+ Dx + E 2025The points (2,3) and (-4,- 4 3 ) lie on the opposite sides of the line L 5 x -6 y + k =0 and k is an integer. If the points (1,2) and (4,5) lie on the same side of the line L =0 , 2025 Full Straight Lines list All COMEDK PYQs