Question

Line segment AB is divided by point P in the ratio of 1:4. Point A is (7,5) and point P is (10, 14). What are the coordinates of point B?

Answer 1

Ответ:

B(22; 50)

Объяснение:

λ = 0.25

B(x, y)

$></p> <p>10 = (7 + 0.25x)/1.25</p> <p>12.5 - 7 = 0.25x</p> <p>x = 5.5 · 4</p> <p>x = 22</p> <p>14 = (5 + 0.25y)/1.25</p> <p>14 · 1.25 - 5 = 0.25y</p> <p>y = 12.5 ÷ 0.25</p> <p>y = 50 </p> </div> <div class=$ 0 0

Answer 2

To find the coordinates of point B, we can use the concept of the section formula. The section formula states that if a line segment AB is divided by a point P in the ratio of m:n, then the coordinates of point P can be calculated using the following formula:

Px = (mx2 + nx1) / (m + n) Py = (my2 + ny1) / (m + n)

Given that the ratio is 1:4, which means m = 1 and n = 4, the coordinates of point A are (x1, y1) = (7, 5), and the coordinates of point P are (x2, y2) = (10, 14), we can substitute these values into the section formula to find the coordinates of point B:

Bx = (1 * 10 + 4 * 7) / (1 + 4) = (10 + 28) / 5 = 38 / 5 = 7.6

By = (1 * 14 + 4 * 5) / (1 + 4) = (14 + 20) / 5 = 34 / 5 = 6.8

Therefore, the coordinates of point B are approximately (7.6, 6.8).