if the slope of the line joining the points (x,5) and (-1,2) is 3/4.Find the value of x. Also determine the distance between them.
Answers
Step-by-step explanation:
Given :-
The slope of the line joining the points (x,5) and (-1,2) is 3/4.
To find :-
i) Find the value of x.
ii) Determine the distance between them.
Solution:-
Given points are (x,5) and (-1,2)
Let (x1, y1)=(x,5)=>x1 = x and y1 = 5
Let (x2, y2)=(-1,2)=>x2=-1 and y2 = 2
We know that
The slope of a linesegment joining the points
(x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)
On Substituting these values in the above formula
=> Slope = (2-5)/(-1-x)
=> Slope = -3/(-1-x)
=> Slope = -3/-(1+x)
=> Slope = 3/(1+x)
According to the given problem
The slope = 3/4
=> 3/(1+x) = 3/4
=> 1/(1+x) = 1/4
=>1+x = 4
=> x = 4-1
=> x = 3
Therefore, x = 3
Now the points are (3,5) and (-1,2)
We know that
The distance between two points (x1, y1) and
(x2, y2) is √[(x2-x1)^2+(y2-y1)^2] units
Let (x1, y1)=(3,5)=>x1 = 3 and y1 = 5
Let (x2, y2)=(-1,2)=>x2=-1 and y2 = 2
Distance = √[(-1-3)^2+(2-5)^2]
=> √[(-4)^2+(-3)^2]
=> √(16+9)
=> √25
=> 5 units
Answer:-
The value of x for the given problem is 3
The distance between the two points is 5 units
Used formulae:-
Slope :-
The slope of a linesegment joining the points
(x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)
Distance formula:
The distance between two points (x1, y1) and
(x2, y2) is √[(x2-x1)^2+(y2-y1)^2] units
Given :-
The slope of the line joining the points (x,5) and (-1,2) is 3/4.
To find :-
i) Find the value of x.
ii) Determine the distance between them.
Solution:-
Given points are (x,5) and (-1,2)
Let (x1, y1)=(x,5)=>x1 = x and y1 = 5
Let (x2, y2)=(-1,2)=>x2=-1 and y2 = 2
We know that
The slope of a linesegment joining the points
(x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)
On Substituting these values in the above formula
=> Slope = (2-5)/(-1-x)
=> Slope = -3/(-1-x)
=> Slope = -3/-(1+x)
=> Slope = 3/(1+x)
According to the given problem
The slope = 3/4
=> 3/(1+x) = 3/4
=> 1/(1+x) = 1/4
=>1+x = 4
=> x = 4-1
=> x = 3
Therefore, x = 3
Now the points are (3,5) and (-1,2)
We know that
The distance between two points (x1, y1) and
(x2, y2) is √[(x2-x1)^2+(y2-y1)^2] units
Let (x1, y1)=(3,5)=>x1 = 3 and y1 = 5
Let (x2, y2)=(-1,2)=>x2=-1 and y2 = 2
Distance = √[(-1-3)^2+(2-5)^2]
=> √[(-4)^2+(-3)^2]
=> √(16+9)
=> √25
=> 5 units
Answer:-
The value of x for the given problem is 3
The distance between the two points is 5 units
Used formulae:-
Slope :-
The slope of a linesegment joining the points
(x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)
Distance formula:
The distance between two points (x1, y1) and
(x2, y2) is √[(x2-x1)^2+(y2-y1)^2] units