advertisement

MCV4U1-UNIT NINE-LESSON FIVE Lesson Five: Distance Formulas Distance from a point to a line in 2 : P d proj n OP n A, B Ax+By+c=0 O OP n Ax1 By 1 C d proj n OP n A2 B 2 Distance from a point to a line in 3 : Q d d θ P sin d PQ d PQ sin and recall magnitude of cross product ...... d PQ d PQ sin d PQ sin d PQ d PQ d PQ d PQ d QP d d We can drop the absolute value bars on sinθ, b/c here, θ will always be between 0° and 180°. MCV4U1-UNIT NINE-LESSON FIVE Distance from a point to a plane: The distance from a point to a plane is....... AX n d n where A is the external point and X is a point on the plane. Example: Find the distance from the point (-1,0,3) to the plane x-3y+2z-1=0 AX n d n A=(-1,0,3), X=any point on the plane.... let y=0,z=0, then x=1, so X=(1,0,0) d 2,0,3 1,3,2 14 AX 2,0,3 , 4 14 n 1,3,2 4 4 14 2 14 14 7 14 n 14