Question

Given directed line segment KM , find the coordinates of L such that the ratio of KL to KM is 1:3. Plot point L. the points are K(-4,7) M(4,-5)

Answer 1

To find the coordinates of point L that divide line segment KM in a 1:3 ratio, we first calculate the change in x and y between points K and M. Then, we divide the change by 4 to find the change in x and y for each unit of the ratio. Finally, we add the change in x and y to the coordinates of K to get the coordinates of L.

Step-by-step explanation:

To find the coordinates of point L, we need to find the coordinates that divide the line segment KM in a 1:3 ratio. First, we find the difference in x-coordinates and y-coordinates between K and M:

Δx = 4 - (-4) = 8

Δy = -5 - 7 = -12

Next, we divide the difference in x-coordinates and y-coordinates by 4 (1 + 3) to find the change in x and y for each unit of the ratio:

change in x = Δx/4 = 8/4 = 2

change in y = Δy/4 = -12/4 = -3

Now, starting from K(-4, 7), we add 2 units of change in x and -3 units of change in y to find the coordinates of L:

L(x, y) = (-4 + 2, 7 - 3)

L(x, y) = (-2, 4)

Therefore, the coordinates of point L are (-2, 4).

Answer 2

From (-4,-9) to (1,1), Δx = 5 and Δy = 10. If we divide the line into 5 equal pieces, each piece is increased by Δx = 1 and Δy = 2 from the previous point. After 3 pieces, the coordinates are (-4+3,-9+6) which is 3/5 of the total length with 2/5 remaining.

Step-by-step explanation: