a(-4,3) b(2,1) m:n=3:5 by section formula
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Answer:
okk
Section Formula
Let us consider two points A (x1, y1, z1) and B(x2, y2, z2). Consider a point P(x, y, z) dividing AB in the ratio m:n as shown in the figure given below.
Section Formula
To determine the coordinates of the point P, the following steps are followed:
Section Formula in 3D
Draw AL, PN, and BM perpendicular to XY plane such that AL || PN || BM as shown above.
The points L, M and N lie on the straight line formed due to the intersection of a plane containing AL, PN and BM and XY- plane.
From point P, a line segment ST is drawn such that it is parallel to LM.
ST intersects AL externally at S, and it intersects BM at T internally.
Since ST is parallel to LM and AL || PN || BM, therefore, the quadrilaterals LNPS and NMTP qualify as parallelograms.
Also, ∆ASP ~∆BTP therefore,
mn=APBP=ASBT=SL–ALBM–TM=NP–ALBM–PN=z–z1z2–z
Rearranging the above equation we get,
z=mz2+nz1m+n
The above procedure can be repeated by drawing perpendiculars to XZ and YZ- planes to get the x and y coordinates of the point P that divides the line segment AB in the ratio m:n internally.
x=mx2+nx1m+n,y=my2+ny1m+n
hope this will help you
Answer:
Section formula is used to find the ratio in which a line segment is divided by a point internally or externally.
x= mx2 + nx1. y= my²+ny1
m+n. m+ n