Question

Given A(−1,2)
and B(3,6)
, find the coordinates of point X
on AB¯¯¯¯¯¯¯¯
such that the ratio of AX
to XB
is 3:5.(1 point)
Responses

(112,112)

left paren 1 Start Fraction 1 over 2 End Fraction comma 1 start fraction 1 over 2 end fraction right paren

(125,425)

left paren 1 Start Fraction 2 over 5 End Fraction comma 4 start fraction 2 over 5 end fraction right paren

(−14,312)

left paren negative Start Fraction 1 over 4 End Fraction comma 3 start fraction 1 over 2 right paren

(12,312)

Answer 1

Use the section formula. With A(−1,2), B(3,6) and AX:XB = 3:5 (m=3, n=5),

x = (n*x1 + m*x2)/(m+n) = (5(−1) + 3(3))/8 = 4/8 = 1/2
y = (5·2 + 3·6)/8 = 28/8 = 7/2

So X = (1/2, 7/2), which corresponds to the choice (1/2, 3 1/2).