Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202423 May 2024Morning ShiftMathematicsStraight LinesActual

The equations of the perpendicular bisectors of the sides AB and AC of ABC are x-y+5=0 and x+2 y=0 respectively. If the coordinates of A are (1,-2) , then the equation of the line B C is

Options

  1. A14 x+23 y-40=0
  2. B13 x-9 y-14=0
  3. C9 x-14 y-25=0
  4. D8 x+15 y-30=0

Correct answer

A. 14 x+23 y-40=0

Step-by-step solution

A B line is perpendicular to E O and passes through vertex A , equation of A B is x+y+1=0 Co-ordinates of E= ( x₁+1 2 , y₁-2 2 ) which is also intersection point of A B with aligned & x-y+5=0 . So, x₁+1 2 =-3 ; y₁-2 2 =2 & (x₁, y₁ )=(-7,6) aligned Similarly, equation of A C is y=2 x-4 And co-ordinates of F= ( x₂+1 2 , y₂-2 2 ) Which is also intersection point of A C with x+2 y=0 So, x₂+1 2 = 8 5 ; y₂-2 2 = 4 5 (x₂, y₂ )= ( 11 5 , 2 5 ) So, the equation of side B C : y-6= 2 5 -6 11 5 +7 (x+7) 14 x+23 y-40=0

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