Question

Помогите пожалуйста!!! На координатном луче отмечены точки A(357) и D(437).Точки B и C,которые расположены на отрезке AD,делят его в отношении 12:!13:15.Найдите координаты точек B и C. (мне нужно знать само решение)

Answer 1

AB/AD=12; BC/AD=13; CD/AD=15.весь отрезок составляет AD= AB+BC+CD=40; расстояние между точками равно 437-357= 80;
40x=80
x=80/40
x=2
12*2=24 -ab,
13*2=26- bc,
15*2=30-cd;
357+24=381-координаты точки B;
381+26=407- координаты точки С.

Answer 2

Problem Analysis

We are given two points, A(357) and D(437), on a coordinate line. We need to find the coordinates of points B and C, which divide the line segment AD in the ratio 12:13:15.

Solution

To find the coordinates of points B and C, we need to determine the distances AB and BC. Let's assume the coordinates of point B are (x, y) and the coordinates of point C are (z, w).

The distance AB can be calculated using the formula: AB = (13 / (12 + 13)) * AD

Similarly, the distance BC can be calculated using the formula: BC = (15 / (12 + 13 + 15)) * AD

To find the coordinates of point B, we can use the following formula: x = (AB / AD) * (Dx - Ax) + Ax y = (AB / AD) * (Dy - Ay) + Ay

To find the coordinates of point C, we can use the following formula: z = (BC / AD) * (Dx - Ax) + Ax w = (BC / AD) * (Dy - Ay) + Ay

Now, let's substitute the given values and calculate the coordinates of points B and C.

Given: Point A: (357) Point D: (437) Ratio: 12:13:15

Calculations: AD = D - A = 437 - 357 = 80

AB = (13 / (12 + 13)) * AD = (13 / 25) * 80 = 41.6 BC = (15 / (12 + 13 + 15)) * AD = (15 / 40) * 80 = 30

x = (AB / AD) * (Dx - Ax) + Ax = (41.6 / 80) * (437 - 357) + 357 = 37.12 + 357 = 394.12 y = (AB / AD) * (Dy - Ay) + Ay = (41.6 / 80) * (0 - 0) + 0 = 0

z = (BC / AD) * (Dx - Ax) + Ax = (30 / 80) * (437 - 357) + 357 = 11.25 + 357 = 368.25 w = (BC / AD) * (Dy - Ay) + Ay = (30 / 80) * (0 - 0) + 0 = 0

Therefore, the coordinates of point B are (394.12, 0) and the coordinates of point C are (368.25, 0).

Answer: The coordinates of point B are (394.12, 0) and the coordinates of point C are (368.25, 0).