Question

What are the coordinates of the point on the directed line segmant from (3,2) to (7,-6) that partitions the segmant into a ratio of 3 to 5​

Answer 1

To find the coordinates of the point that partitions the line segment into a ratio of 3 to 5, we can use the formula: x = (5ax2 + 3bx1)/(3a + 5b) and y = (5ay2 + 3by1)/(3a + 5b). Plugging in the values, we get x = 4 and y = -2. Therefore, the coordinates of the point are (4, -2).

Step-by-step explanation:

To find the coordinates of the point that partitions the line segment into a ratio of 3 to 5, we can use the formula:

x = (5ax2 + 3bx1)/(3a + 5b)
y = (5ay2 + 3by1)/(3a + 5b)

Here, (x1, y1) represents the coordinates of the first point (3, 2), and (x2, y2) represents the coordinates of the second point (7, -6).

Plugging in the values, we get:

x = (5*7 + 3*3)/(3*5 + 5*3) = 4
y = (5*-6 + 3*2)/(3*5 + 5*3) = -2

Therefore, the coordinates of the point that partitions the line segment into a ratio of 3 to 5 are (4, -2).