Answer:
C (25,-13)
Step-by-step explanation:
To find the value of x in the coordinate C(x, -13), we can use the fact that points A, B, and C are collinear, meaning they lie on the same line.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Using the coordinates of points A(-2,5) and B(1,3), we can calculate the slope of the line passing through them:
slope = (3 - 5) / (1 - (-2))
slope = -2 / 3
Since points A, B, and C are collinear, they all lie on the same line, and therefore have the same slope. So we can use the slope we calculated to find the value of x for point C.
Using the slope (-2/3) and the y-coordinate of point A (5), we can use the point-slope form of a linear equation to find the equation of the line passing through A and B:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Using point A(-2,5):
y - 5 = (-2/3)(x - (-2))
y - 5 = (-2/3)(x + 2)
Simplifying the equation:
3(y - 5) = -2(x + 2)
3y - 15 = -2x - 4
3y = -2x + 11
Now we can substitute the y-coordinate of point C (-13) into the equation to solve for x:
3(-13) = -2x + 11
-39 = -2x + 11
-50 = -2x
x = 25
Therefore, the value of x in the coordinate C(x, -13) is 25.
