If the line joining the points (2,4)and (5,-2)is parallel to the line joining (-1,-2)and(p,6)find the value of p
Answers
Step-by-step explanation:
Given :-
The line joining the points (2,4) and (5,-2) is parallel to the line joining (-1,-2) and
(p,6).
To find :-
Find the value of p?
Solution :-
Given that
The line joining the points (2,4) and (5,-2) is parallel to the line joining (-1,-2) and
(p,6).
We know that
If two lines are parallel then the slopes of the two lines are equal.
Slope of the first line :-
Let (x1, y1) = (2,4) => x1 = 2 and y1 = 4
Let (x2, y2) = (5,-2) => x2 = 5 and y2 = -2
We know that
The slope of the line joining the points (x1, y1) and (x2, y2) is (y2-y1)/ (x2-x1)
Slope = (-2-4)/(5-2)
=> Slope = -6/3
=> Slope = -2
Slope of the second line :-
Let (x1, y1) = (-1,-2) => x1 = -1 and y1 = -2
Let (x2, y2) = (p,6) => x2 = p and y2 = 6
We know that
The slope of the line joining the points
(x1, y1) and (x2, y2) is (y2-y1)/ (x2-x1)
Slope = (6-(-2))/(p-(-1))
=> Slope = (6+2)/(p+1)
=> Slope = 8/(p+1)
We have,
Slope of the 1st line=Slope of the 2nd line
=> -2 = 8/(p+1)
=> -2 × (p+1) = 8
=> p+1 = 8/-2
=> p+1 = -4
=> p = -4-1
=> p = -5
Therefore, p = -5
Answer:-
The value of p for the given problem is -5
Used Concept :-
→ If two lines are parallel then the slopes of the two lines are equal.
Used formulae:-
→ The slope of the line joining the points (x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)
Step-by-step explanation:
Given that
The line joining the points (2,4) and (5,-2) is parallel to the line joining (-1,-2) and
(p,6).
We know that
If two lines are parallel then the slopes of the two lines are equal.
Slope of the first line :
Let (x1, y1) = (2,4) => x1 = 2 and y1 = 4
Let (x2, y2) = (5,-2) => x2 = 5 and y2 = -2
We know that
The slope of the line joining the points
(x1, y1) and (x2, y2) is (y2-y1)/ (x2-x1)
Slope = (-2-4)/(5-2) -
=> Slope = -6/3
=> Slope = -2
Slope of the second line :
Let (x1, y1)= (-1,-2) => x1 = -1 and y1 = -2
Let (x2, y2) = (p,6) => x2 = p and y2 = 6
We know that
The slope of the line joining the points (x1, y1) and (x2, y2) is (y2-y1)/ (x2-x1)
=> Slope = -2
Slope of the second line :
Let (x1, y1) = (-1,-2) => x1 = -1 and y1 = -2
Let (x2, y2) = (p,6) => x2 = p and y2 = 6
We know that
The slope of the line joining the points (x1, y1) and (x2, y2) is (y2-y1)/ (x2-x1)
Slope = (6-(-2))/(p-(-1))
=> Slope = (6+2)/(p+1) => Slope = 8/(p+1)
We have,
Slope of the 1st line-Slope of the 2nd line
=> -2 = 8/(p+1)
=> -2x (p+1) = 8
=> p+1 = 8/-2
=> p+1 = -4
=> p = -4-1
=> p = -5
Therefore, p = -5
Answer:
The value of p for the given problem is -5