The three coordinate points are collinear. Use slopes to write aproportion to find the value of a.
#38. (-4,1),(-1,2),(5,a)
#39. (4,5),(1,2),(a,0)
#38
(a-2)/(5+1) = (2-1)/(-1+4)
(a-2)/6 = 1/3
3a - 6 = 6
a = 4
Do #39 the same way, let me know what you got
To determine if the three coordinate points are collinear, we need to check if the slopes between any two pairs of points are equal. If they are, it indicates that the points lie on the same line.
Let's first find the slopes between the given points in each question:
#38. (-4,1), (-1,2), (5,a)
The slope between the first two points can be found using the slope formula:
m₁ = (y₂ - y₁) / (x₂ - x₁)
Using (-4,1) and (-1,2):
m₁ = (2 - 1) / (-1 + 4) = 1 / 3
Next, let's find the slope between the second and third points, which will involve the variable 'a':
m₂ = (a - 2) / (5 - (-1)) = (a - 2) / 6
Since the three points are collinear, the slopes should be equal, so we can set up a proportion with these slopes:
1 / 3 = (a - 2) / 6
To solve for 'a', we can cross-multiply and solve the resulting equation. Multiply both sides of the equation by 6 to get:
2 = (a - 2) * (1 / 3)
Multiply both sides by 3:
6 = a - 2
Add 2 to both sides:
a = 8
Thus, the value of 'a' is 8.
#39. (4,5), (1,2), (a,0)
Using the same approach as above, we need to find the slopes between different pairs of points:
The slope between (4,5) and (1,2) is:
m₁ = (2 - 5) / (1 - 4) = -3 / -3 = 1
The slope between (1,2) and (a,0) is calculated as:
m₂ = (0 - 2) / (a - 1) = -2 / (a - 1)
Since the three points are collinear, the slopes should be equal, so we can set up a proportion:
1 = -2 / (a - 1)
To solve for 'a', we can cross-multiply and solve the resulting equation:
1 * (a - 1) = -2
a - 1 = -2
Add 1 to both sides:
a = -1
Therefore, the value of 'a' is -1