Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202119 Aug 2021Evening ShiftMathematicsStraight LinesActual

The ratio in which the straight line 3 x + 4 y = 6 divides the join of the points ( 2 , - 1 ) and ( 1 , 1 ) is

Options

  1. A1 : 4
  2. B8 : 13
  3. C4 : 1
  4. D− 4 : 1

Correct answer

C. 4 : 1

Step-by-step solution

Let, the line 3 x + 4 y = 6 divides the line segment joining the points P 2 ,   - 1 and Q 1 ,   1 in ratio k   :   1 . Hence, the point of intersection is 2 + k k + 1 ,   - 1 + k k + 1 , which lies on the line 3 x + 4 y = 6 . So, 3 2 + k k + 1 + 4 - 1 + k k + 1 = 6   ⇒   6 + 3 k - 4 + 4 k = 6 k + 6   ⇒ k = 4 Hence, the ratio is 4   :   1 .

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 AP EAMCET PYQs