Question

Трикутник ABC задано координатами вершин А(1;3), В(4;-2), С(-8;1). знайдіть довжину висоти АD трикутника АВС, якшо відомо, що ордината точки D на 1 одиничний відрізок менша від її абсциси

Answer 1

Какое количество осадков? в какое время выпадают в Алжире ?

Answer 2

I have searched the web for your question and found some relevant results. Here is a summary of what I learned:

- To find the length of the height AD of the triangle ABC, we need to know the equation of the side BC and the coordinates of the point D. - The equation of the side BC can be found by using the formula `(y - y1) / (y2 - y1) = (x - x1) / (x2 - x1)`, where `(x1, y1)` and `(x2, y2)` are the coordinates of the vertices B and C respectively. Substituting the given values, we get `(y + 2) / 3 = (x - 4) / (-12)`, or `12y + 24 = -3x + 12`, or `3x + 12y + 12 = 0`. - The coordinates of the point D can be found by using the given condition that the ordinate of D is one unit less than its abscissa. That is, `y = x - 1`. Substituting this into the equation of BC, we get `3x + 12(x - 1) + 12 = 0`, or `15x - 12 = 0`, or `x = 4/5`. Therefore, `y = 4/5 - 1 = -1/5`. Hence, the point D has the coordinates `(4/5, -1/5)`. - The length of the height AD can be found by using the distance formula between two points: `d = sqrt((x2 - x1)^2 + (y2 - y1)^2)`, where `(x1, y1)` and `(x2, y2)` are the coordinates of the points A and D respectively. Substituting the given values, we get `d = sqrt((4/5 - 1)^2 + (-1/5 - 3)^2)`, or `d = sqrt(169/25 + 676/25)`, or `d = sqrt(845/25)`, or `d = sqrt(169) / 5`, or `d = 13 / 5`.

Therefore, the length of the height AD of the triangle ABC is 13 / 5 units. I hope this helps you understand the solution.