Look the graph in uploaded file-
Write the equations of the lines p & r n the graph:
A student answered equation of line'q' as x + y=1.Did he answer correctly?Also, find the area enclosed between lines p,q& r.
Answers
Given : A graph showing 3 lines p , q & r
To find : is line 1 is x + y = 1
equations of the lines p & r
area enclosed between lines p,q& r.
Solution:
Line q has point (0,1) & ( 1, 0)
Slope = (0- 1)/(1 - 0) = - 1
Line P
y - 1 = - 1(x-0)
=> y - 1 = -x
=> x + y = 1
Yes line q is x + y = 1
student answered equation of line'q' as x + y=1 correctly
Line p
x = - 1
Line r
y = - 2
x + y = 1
x = - 1
y = - 2
(-1 , - 2) , ( 3 , - 2) & ( -1 , 2)
a right angle triangle is formed by lines with each side = 4
Area = (1/2) * 4 * 4 = 8 sq units
or
(-1 , - 2) , ( 3 , - 2) & ( -1 , 2)
Area = (1/2) | -1 (-2 - 2) + 3(2-(-2)) -1(-2 -(-2))|
= (1/2) | 4 + 12 - 0 |
= 16/2
= 8 sq units
area enclosed between lines p,q& r. = 8 sq units
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Answer:
Given : A graph showing 3 lines p, q & r
To find : is line 1 is x + y = 1
equations of the lines p & r
area enclosed between lines p,q& r.
Solution:
Line q has point (0,1) & ( 1, 0)
Slope = (0- 1)/(1 - 0) = - 1
Line P
y - 1 = - 1(x-0)
=> y - 1 = -x
=> x + y = 1
Yes line q is x + y = 1
student answered equation of line'q' as x + y=1 correctly
Line p
x = - 1
Line r
y = - 2
x + y = 1
x = - 1
y = - 2
(-1 , - 2) , ( 3 , - 2) & ( -1 , 2)
a right angle triangle is formed by lines with each side = 4
Area = (1/2) * 4 * 4 = 8 sq units
or
(-1 , - 2) , ( 3 , - 2) & ( -1 , 2)
Area = (1/2) | -1 (-2 - 2) + 3(2-(-2)) -1(-2 -(-2))|
= (1/2) | 4 + 12 - 0 |
= 16/2
= 8 sq units
area enclosed between lines p,q& r. = 8 sq units