Question

# (i) Find the coordinates of the point which divies the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3. (ii) Find the coordinates of the point which divides the join of A (-5, 11) and B(4, -7) in the ratio 7 : 2.

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Solution

## (i)The endpoints of AB are A (−1,7) and B (4,−3) Therefore, (x1=−1,y1=7) and (x2=4,y2=−3) Also, m=2 and n=3 Let the required point be P(x,y) By section formula, we get x=mx2+nx1m+n, y=my2+ny1m+n ⇒ x=(2×4)+(3×−1)2+3, y=(2×−3)+(3×7)2+3 ⇒x=8−35,y=−6+215 ⇒x=55,y=155 Therefore, x = 1 and y = 3 Hence, the coordinates of the required point are (1,3) (ii)The endpoints of AB are A (−5,11) and B (4,−7) Therefore, (x1=−5,y1=11) and (x2=4,y2=−7) Also, m=7 and n=2 Let the required point be P(x,y) By section formula, we get x=mx2+nx1m+n, y=my2+ny1m+n ⇒ x=(7×4)+(2×−5)7+2, y=(7×−7)+(2×11)7+2 ⇒x=28−109,y=49+229 ⇒x=189,y=−279 Therefore, x = 2 and y = -3 Hence, the coordinates of the required point are (2,-3)

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