Question

Given A(−1,2) 𝐴 ( − 1 , 2 ) and B(3,6) 𝐵 ( 3 , 6 ) , find the coordinates of point X 𝑋 on AB¯¯¯¯¯¯¯¯ 𝐴 𝐵 ¯ such that the ratio of AX 𝐴 𝑋 to XB 𝑋 𝐵 is 3:5.(1 point) Responses (112,112) ( 1 1 2 , 1 1 2 ) left paren 1 Start Fraction 1 over 2 End Fraction comma 1 start fraction 1 over 2 end fraction right paren (12,312) ( 1 2 , 3 1 2 ) left paren Start Fraction 1 over 2 End Fraction comma 3 start fraction 1 over 2 right paren (−14,312) ( − 1 4 , 3 1 2 ) left paren negative Start Fraction 1 over 4 End Fraction comma 3 start fraction 1 over 2 right paren (125,425)

Answer 1

Vector AB = (4,4). X = A + (3/(3+5))·AB = (-1,2) + (3/8)(4,4) = (-1,2) + (3/2,3/2) = (1/2,7/2) = (1/2,3 1/2). So the correct choice is (1/2, 3 1/2).