for a car driving at a constant rate of 60 miles per hour, the table represents distance from a historical mile marker on the hi
ghway as a function of dribing time. which equation could be used to determine the driving time(s) when the car is 150 miles from the historical mile marker?
1 answer:
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Answer:
Circumcenter =(-1,0)
Orthocenter =(2,-3)
Step-by-step explanation:
Given : Points A = (2,3), B = (-4,-3), C = (2,-3)
Formula used :
→Mid point of two points-
→Slope of two points -
→Perpendicular of a line =
Circumcenter- The point where the perpendicular bisectors of a triangle meets.
Orthocenter-The intersecting point for all the altitudes of the triangle.
To find out the circumcenter we have to solve any two bisector equations.
We solve for line AB and AC
So, mid point of AB =
Slope of AB =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of the perpendicular bisector = -1
Equation of AB with slope -1 and the coordinates (-1,0) is,
(y – 0) = -1(x – (-1))
y+x=-1………………(1)
Similarly, for AC
Mid point of AC =
Slope of AC =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of the perpendicular bisector = 0
Equation of AC with slope 0 and the coordinates (2,0) is,
(y – 0) = 0(x – 2)
y=0 ………………(2)
By solving equation (1) and (2),
put y=0 in equation (1)
y+x=-1
0+x=-1
⇒x=-1
So the circumcenter(P)= (-1,0)
To find the orthocenter we solve the intersections of altitudes.
We solve for line AB and BC
So, mid point of AB =
Slope of AB =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of CF = -1
Equation of AB with slope -1 and the coordinates (-1,0) gives equation CF
(y – 0) = -1(x – (-1))
y+x=-1………………(3)
Similarly, mid point of BC =
Slope of AB =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of AD = 0
Equation of AB with slope 0 and the coordinates (-1,-3) gives equation AD
(y-(-3)) = 0(x – (-1))
y+3=0
y=-3………………(4)
Solve equation (3) and (4),
Put y=-3 in equation (3)
y+x=-1
-3+x=-1
x=2
Therefore, orthocenter(O)= (2,-3)
In the question, we are given with speed of a car and the distance it have to travel.
Given:
- Speed of the car = 40 km/hr.
- Distance to travel = 60 km
So, we can say that in 1 hour, the car can travel 40 km. And we have to find the time taken by the car to travel 60 km.
This can be easily done by using the Speed, Distance and Time formula which says:
So, let's solve by using this formula.
⇛ s = v × t
⇛ 60 km = 40 km/hr × t
⇛ t = 60 km / 40 km/hr
⇛ t = 3/2 hr.
⇛ t = 90 mins or 1 1/2 hours
So, time the car will take to travel 60 km:
And we are done !!
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