Question

Төбелері: 1)А(0,1),В(1;-4),С(5;х) 2)А(-4;1),В(-2;4),С(0;х) нүктелері болатын АВС ұшбұрышының тең бүйірлі екені белгілі болса, х-ті табыңдар

Answer 1

Task: Find the value of x in the given coordinates

To find the value of x in the given coordinates, we can use the fact that the coordinates of points A, B, and C lie on the same line. This means that the slope of the line passing through A and B is equal to the slope of the line passing through B and C.

Let's consider the first set of coordinates: A(0,1), B(1,-4), C(5,x).

The slope of the line passing through A and B can be calculated using the formula:

slope_AB = (y2 - y1) / (x2 - x1)

Substituting the coordinates of A and B into the formula, we get:

slope_AB = (-4 - 1) / (1 - 0) = -5

Similarly, the slope of the line passing through B and C can be calculated using the formula:

slope_BC = (y3 - y2) / (x3 - x2)

Substituting the coordinates of B and C into the formula, we get:

slope_BC = (x + 4) / (5 - 1) = (x + 4) / 4

Since the slopes of the two lines are equal, we can equate them:

-5 = (x + 4) / 4

To solve for x, we can cross-multiply and simplify the equation:

-5 * 4 = x + 4

-20 = x + 4

x = -20 - 4

x = -24

Therefore, the value of x in the first set of coordinates A(0,1), B(1,-4), C(5,x) is -24.

Let's move on to the second set of coordinates.