In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz
ontal, what are the coordinates of point C? A. (5, -3) B. (2, -3) C. (7, -1) D. (2, -1)
2 answers:
Answer: D. (2,-1)
Step-by-step explanation:
Given: In the diagram, point D divides line segment AB in the ratio of 5:3.
Since, line segment AC is vertical then the x coordinate of C will be same as A (2) and line segment CD is horizontal then the y coordinate of C will be same as D.
Coordinates of A = (2,-6)
Coordinates of B = (10,2)
Section formula: If a point P(x,y) divides a line segment MN with in ration m:n, then
Using section formula, we have
The y coordinate of D =
Thus, the coordinates of C =(2,-1)
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<u>Solution-</u>
The company purchased a new computer for $1500 and chooses to depreciate using the straight-line method for 5 years.
a-
As the value is depreciating, so its slope will be -ve.
( ∵ The value of 1500 will depreciate in 5 years )
y-intercept = 1500 ( ∵ At the beginning when x=0, y=1500)
Linear equation of the system,
y = mx +c ,
where,
m = slope = -300,
c = y-intercept = 1500
Putting the values,
b-
The implied domain of the function is 1≤x≤5 or [1,5]
c-
Follow the attachment attached herewith for the graph.
d-
Here,
y = the value of the computer
.
x = number of years depreciated = 3
Putting the values in the linear equation,
y = 1500-300(3) = 1500-900 = 600
∴ The book value of the computer after 3 years is $600.
e-
Here given that,
y = value of computer = 1600
x = asked = ??
Putting the values in the equation,
1600 = 1500 - 300x
⇒ 100= -300x
⇒ x= -3
∴ As the x is in negative, i.e it is impossible for the computer to be worth of 1600. It happens also because as the value is depreciating, it will always be less than 1500.