Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2010MathematicsStraight Lines

The image of the point (4,-13) with respect to the line 5 x+y+6=0 is

Options

  1. A(-1,-14)
  2. B(3,4)
  3. C(1,2)
  4. D(-4,13)

Correct answer

A. (-1,-14)

Step-by-step solution

Since, Q is the mid point of P P^ , then Q= ( x₁+4 2 , y₁-13 2 ) Also Q lies on the A B , then 5 ( x₁+4 2 )+ ( y₁-13 2 )+6=05 x₁+20+y₁-13+12=05 x₁+y₁+19=0 (i) Since, line P P^ is perpendicular to A B , then (Slope of A B) ( . Slope of .P P^ )=-1(-5) ( y₁+13 x₁-4 )=-15 y₁+65=x₁-4x₁-5 y₁-69=0 (ii) Solving Eqs. (i) and (ii), we get array r 25 x₁+5 y₁+95=0 x₁-5 y₁-69=0 26 x₁+26=0 array x₁=-1 From Eq.(ii) 5 y₁=-1-695 y₁=-70y₁=-14 So, image of the point p with respect to A B is (-1,-14)

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