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

(12,312)

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

(112,112)

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

(125,425)

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

Use the section formula (or vector fraction). AX : AB = 3/(3+5) = 3/8, so
X = A + (3/8)(B − A)
= (−1,2) + (3/8)(4,4)
= (−1 + 12/8, 2 + 12/8)
= (1/2, 7/2) = (1/2, 3 1/2).

So the correct choice is (1/2, 3 1/2).