find the coordinates of point P that lies on the line segment MQ, M(5,-2), Q(-2,12), and partitions the segment at a ratio of 2:5
MP is 2/7 of the way from M to Q
The distance from M to Q is Q-M
So, P = M + 2/7 (Q-M)
Thus, the x-coordinate of P is
x = 5 + 2/7 (-2-5) = 5 - 2 = 3
and y = -2 + 2/7 (12+2) = -2+4 = 2
P = (3,2)
Point P lies on Line Segment NM. Point N is located at (- 2, - 6) and Point Mis located at * (5, 8), 1f; NP / P * M = 5/2 (the line partitions in a 5:2 ratio) . Where is point P located on Line NM?*
To find the coordinates of point P that partitions the line segment MQ at a ratio of 2:5, we can use the section formula.
Let's assume that point P has coordinates (x, y).
According to the section formula, the coordinates of point P can be found using the following formula:
x = ((5 * 5) + (-2 * -2) + (2 * -2)) / (2 + 5)
y = ((2 * 12) + (-2 * -2) + (5 * -2)) / (2 + 5)
Simplifying these equations further:
x = (25 + 4 - 4) / 7
y = (24 + 4 - 10) / 7
x = 25 / 7
y = 18 / 7
So, the coordinates of point P are (25/7, 18/7).
To find the coordinates of point P that partitions the line segment MQ at a ratio of 2:5, we can use the section formula. The section formula states that if we have two points A(x1, y1) and B(x2, y2), and we want to find the coordinates of a point P that partitions the line segment AB at a ratio of m:n, then the coordinates of point P can be obtained using the following formulas:
Px = (mx2 + nx1) / (m + n)
Py = (my2 + ny1) / (m + n)
In our case, we have point M(5, -2), Q(-2, 12), and we want to partition MQ at a ratio of 2:5. Therefore, m = 2 and n = 5.
Using the section formula, we can find the coordinates of point P:
Px = (2*(-2) + 5*5) / (2 + 5)
= (-4 + 25) / 7
= 21 / 7
= 3
Py = (2*12 + 5*(-2)) / (2 + 5)
= (24 - 10) / 7
= 14 / 7
= 2
Therefore, the coordinates of point P are (3, 2).