Question

Given points A(1,1)
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.
where is M located

Answer 1

sorry that's incorrect

Answer 2

To find the coordinates of point M, we need to find a point that divides the line AB in a 1:5 ratio.

Let's label the coordinates of point M as (x, y).

We can find the coordinates of M by using the ratio formula:

(x - 1)/(7 - 1) = 1/5

Simplifying the equation, we have:

(x - 1)/6 = 1/5

Cross-multiplying, we get:

5(x - 1) = 6

Expanding, we have:

5x - 5 = 6

Adding 5 to both sides, we get:

5x = 11

Dividing both sides by 5, we find:

x = 11/5

To find y, we can use the ratio formula again:

(y - 1)/(-2 - 1) = 1/5

Simplifying the equation, we have:

(y - 1)/-3 = 1/5

Cross-multiplying, we get:

5(y - 1) = -3

Expanding, we have:

5y - 5 = -3

Adding 5 to both sides, we get:

5y = 2

Dividing both sides by 5, we find:

y = 2/5

Therefore, the coordinates of point M are approximately (2.2, 0.4).

Answer 3

Apologies for the incorrect response earlier. Let's try again to find the coordinates of point M.

To find the coordinates of point M on the line segment AB such that the ratio of AM to MB is 1:5, we can use the section formula.

Let the coordinates of point M be (x, y).

Using the section formula, we can find the x-coordinate of M as follows:

x = (5 * x₁ + 1 * x₂) / (5 + 1) = (5 * 1 + 1 * 7) / 6 = (5 + 7) / 6 = 12 / 6 = 2

Using the same formula, we can find the y-coordinate of M:

y = (5 * y₁ + 1 * y₂) / (5 + 1) = (5 * 1 + 1 * (-2)) / 6 = (5 - 2) / 6 = 3 / 6 = 1/2

Therefore, the coordinates of point M are (2, 1/2), or approximately (2, 0.5).