AP EAMCET20228 Jul 2022Evening ShiftMathematicsStraight LinesActual

Ali points inside the triangle with vertices at (1,3),(5,0) and (-1,2) must necessarily satisfy.

Options

A3 x+2 y 0
B3 x+2 y>0
C2 x-3 y-12>0
D2 x+y-13>0

Correct answer

B. 3 x+2 y>0

Step-by-step solution

Let A (1,3), B (5,0), C (-1,2) For point A(1,3), 3 x+2 y=3+6=9>0 For point B(5,0), 3 x+2 y=15+0=15>0 For point C(-1 ; 2), 3 x+2 y=-3+4=1>0 Option (a) is rejected. Now, for option (c) 2 x-3 y-12=2-9-12 < 0 Option ( c ) is rejected. Also, 2 x+y-13=4+3-13 < 0 Option (d) is rejected. So, option (b) is correct.

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 2025 The 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 2025 The image of a point (2,-1) with respect to the line x-y+1=0 is 2025 If 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 2025 A 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 2025 A (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 2025 By 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 2025 The 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