A B and C D are two line segments, where A(2,3,0), B(6,9,0), C(-6,-9,0) . P and Q are mid-point of A B and C D , respectively and L is the mid-point of P Q . Find the distance of L from the plane 3 x+4 z+25=0

Step-by-step solution

Let coordinate of D is (x, y, z) . Using mid-point formula, aligned Q &= ( x-6 2 , y-9 2 , z+0 2 ) Also, P &= ( 2+6 2 , 3+9 2 , 0+0 2 )=(4,6,0) aligned Since, A C | P Q aligned & D.R'.s of line A C= D.R' s of line P Q & (-8,-12,0)= ( x-14 2 , y-21 2 , z 2 ) & x=-2, y=-3, z=0 & D(-2,-3,0) Q(-4,-6,0) aligned If L is mid-point of P Q , then L ( 4-4 2 , 6-6 2 , 0 )=(0,0,0) Perpendicular distance of L(0,0,0) from the plane 3 x+4 z+25=0 is | 3(0)+4(0)+25 (3)²+(4)² |= | 25 25 |= 25 =5