Question

Point R lies on the directed line segment from L (-8,-10) to M (4,-2) and partitions the segment in the ratio 3 to 5. What are the coordinates of point R

Answer 1

The coordinates of point R which lies on the line segment from L (-8,-10) to M (4,-2) and partitions the segment in the ratio of 3 to 5 are (-3.5, -7), found using the section formula for internal division of a line segment.

Step-by-step explanation:

Point R lies on the directed line segment from L (-8,-10) to M (4,-2) and partitions the segment in the ratio 3 to 5. To find the coordinates of point R, you can use the section formula, which is applied in the context of the internal division of a line segment. According to this formula, if a point R divides a line segment joining points L(x1, y1) and M(x2, y2) in the ratio m:n internally, then the coordinates of point R are given by ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n)).

For this problem, the ratio is 3:5, so point R divides the line segment in the ratio 3 to 5 internally. Using the section formula, the coordinates of R can be calculated as follows:

1. Let's assign m = 3 and n = 5.
2. Plug the values and coordinates into the formula: R = ( (3*4 + 5*(-8)) / (3 + 5), (3*(-2) + 5*(-10)) / (3 + 5) ).
3. Simplify the expression: R = ( (12 - 40) / 8, (-6 - 50) / 8 ).
4. Calculate the coordinates: R = ( -28 / 8, -56 / 8 ).
5. Reduce to the simplest form: R = ( -3.5, -7 ).

Therefore, the coordinates of point R are (-3.5, -7).

Answer 2

R = (- 3.5, - 7 )

Step-by-step explanation:

Using the Section formula

`x_(R)` =
`(3(4)+5(-8))/(3+5)` =
`(12-40)/(8)` =
`(-28)/(8)` = - 3.5

`y_(R)` =
`(3(-2)+5(-10))/(3+5)` =
`(-6-50)/(8)` =
`(-56)/(8)` = - 7

Thus coordinates of R = (- 3.5, - 7 )