Question

A (4, -3) amd B (8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1.

Answer 1

Answer:

let m:n be 3:1

by section formula

x=mx2+nx1 y=my2+ny1

m+n m+n

x = 3(8)+1(4) y=3(5)+1(-3)

3+1 3+1

x=24+4 y=15-3

4 4

x=28 y=12

4 4

x=7 y=3

therefore the points which divides the segment is (7,3)

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Answer 2

• A(4,-3)=x¹,x²
• A(4,-3)=x¹,x²B(8,5)=y¹,y²
• A(4,-3)=x¹,x²B(8,5)=y¹,y² AB=3:4=m:n
• A(4,-3)=x¹,x²B(8,5)=y¹,y² AB=3:4=m:n By section formula
• A(4,-3)=x¹,x²B(8,5)=y¹,y² AB=3:4=m:n By section formula = mx²+nx¹/m+n = my²+ny¹/m+n
• A(4,-3)=x¹,x²B(8,5)=y¹,y² AB=3:4=m:n By section formula = mx²+nx¹/m+n = my²+ny¹/m+n = 3×(-3)+4×4 /3+4 = 3×5+4×8/3+4
• A(4,-3)=x¹,x²B(8,5)=y¹,y² AB=3:4=m:n By section formula = mx²+nx¹/m+n = my²+ny¹/m+n = 3×(-3)+4×4 /3+4 = 3×5+4×8/3+4 = -9+16/7. = 15+32/7
• A(4,-3)=x¹,x²B(8,5)=y¹,y² AB=3:4=m:n By section formula = mx²+nx¹/m+n = my²+ny¹/m+n = 3×(-3)+4×4 /3+4 = 3×5+4×8/3+4 = -9+16/7. = 15+32/7
• A(4,-3)=x¹,x²B(8,5)=y¹,y² AB=3:4=m:n By section formula = mx²+nx¹/m+n = my²+ny¹/m+n = 3×(-3)+4×4 /3+4 = 3×5+4×8/3+4 = -9+16/7. = 15+32/7 = 7/7
• A(4,-3)=x¹,x²B(8,5)=y¹,y² AB=3:4=m:n By section formula = mx²+nx¹/m+n = my²+ny¹/m+n = 3×(-3)+4×4 /3+4 = 3×5+4×8/3+4 = -9+16/7. = 15+32/7 = 7/7= 1

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