AP EAMCET202419 May 2024Evening ShiftMathematicsStraight LinesActual

If L , M , N are the mid points of the sides PQ , QR and RP of PQR respectively. then Q M + L N + M L + R N - M N - Q L =

Options

AP Q + Q R + L M + M N
BL P + P M + M Q
CP Q + Q R - P R
DL M + M N + N R

Correct answer

C. P Q + Q R - P R

Step-by-step solution

In P Q R, M and N are mid-points of Q R and R P So, M N = 1 2 P Q M N = L P = L Q So, N M = P L = L Q Similarly, we get M L = R N = N P and L N = Q M = M R Now, Q M + L N + M L + R N - M N - Q L = Q R + R P -(- P Q )= P Q + Q R - P R .

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