Find the coordinates of point P that lies on the line segment MQ, M(-9, -5), Q(3, 5), and partitions the segment at a ratio of 2 to 5
P = M + 2/7 (Q-M)
P = 5/7 M + 2/7 Q = (5M+2Q)/7
So, for the x value, that would be
(5(-9)+2(3))/7 = -39/7
do y the same way
To find the coordinates of point P that lies on the line segment MQ and partitions the segment at a ratio of 2 to 5, we can use the formula for finding a point on a line segment using the ratio of the distances.
Let's label the coordinates of point P as (x, y). We can find the x-coordinate of P as follows:
x = [(5 * (-9)) + (2 * 3)] / (2 + 5)
= [-45 + 6] / 7
= -39/7
Now, let's find the y-coordinate of P:
y = [(5 * (-5)) + (2 * 5)] / (2 + 5)
= [-25 + 10] / 7
= -15/7
Therefore, the coordinates of point P that lies on the line segment MQ and partitions the segment at a ratio of 2 to 5 are (-39/7, -15/7).
To find the coordinates of point P that lies on the line segment MQ and partitions it at a ratio of 2 to 5, we can use the concept of the section formula. The section formula states that if we have two points A(x1, y1) and B(x2, y2), and a point P divides the line segment AB in the ratio of m:n (where m + n = total ratio), then the coordinates of point P can be found using the following formulas:
Px = (mx2 + nx1) / (m + n)
Py = (my2 + ny1) / (m + n)
In this case, we have point M(-9, -5) with coordinates (x1, y1) and point Q(3, 5) with coordinates (x2, y2). The ratio given is 2:5, which means m = 2 and n = 5.
Substituting these values into the section formula, we can find the coordinates of point P:
Px = (2 * 3 + 5 * -9) / (2 + 5)
= (6 - 45) / 7
= -39 / 7
= -5.571
Py = (2 * 5 + 5 * -5) / (2 + 5)
= (10 - 25) / 7
= -15 / 7
= -2.143
Therefore, the coordinates of point P that partitions the line segment MQ at a ratio of 2 to 5 are approximately (-5.571, -2.143).