Given points A(1,1)

Question

and B(7,−2)
, determine the coordinates of point M
on AB¯¯¯¯¯¯¯¯
such that the ratio of AM
to MB
is 1:5. Write your responses as decimal values (if necessary) to the tenths place.

Answer 1

To find the coordinates of point M on line AB, we can use the formula for finding a point between two given points:

M(x,y) = ( (1/6)*x₁ + (5/6)*x₂ , (1/6)*y₁ + (5/6)*y₂ )

In this case, x₁ = 1, y₁ = 1, x₂ = 7, and y₂ = -2. Plugging these values into the formula, we get:

M(x,y) = ( (1/6)*1 + (5/6)*7 , (1/6)*1 + (5/6)*(-2) )
= ( (1/6) + (5/6)*7 , (1/6) + (5/6)*(-2) )
= ( 1/6 + 35/6 , 1/6 - 10/6 )
= ( 36/6 , -9/6 )
= ( 6 , -1.5 )

Therefore, the coordinates of point M are (6, -1.5).