1ans 1 - k2
ans 2 - 22/9
Plz help
1.find the area of traingle formed by the lines y-x=0;x+y=0 and x-k=0.
2.the line 7x-9y-19=0 is perpendicular to the line through the points(x,3)
and (4,1), find the value of x.
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4 Answers
1for Q.1, solve the equations two at a time to get the respective coordinates of the vertices of the triangle....then use heron's formula.
for Q.2 , make an equation of the line joining the given points, find its slope, and use the relation for slopes of 2 perpendicular lines i.e. m1m2= -1.
11)need not use heron's formula,from equations it can be easily established that the lines y - x=0 and x +y=0 are perpendicular and then we can apply --area=1/2 base x height.
also both these lines intersect at origin and base=height = k√2 (using trignometry)
so area is k2....
2)22/9
1Question : 1
To find the area of triangle OAB ...
It simple because OAB is a right angled triangle..
Area = ( AB) ( OM) / 2
Area = ( 2K) ( K) / 2 = K^2 and.
Question : 2
.the line 7x-9y-19=0 is perpendicular to the line through the points(x,3)
and (4,1), find the value of x.
Two lines having slope m1 and m2 are perpendicular ...then m1.m2 = -1
Now slope of the line passing through (x,3) and (4,1) ...is (3-1)/(x-4) = 2/(x-4)
Slope of the line 7x-9y = 19 is 7/9
SO 2/(x-4) * 7/9 = - 1
or 2/(x-4) = -9/7
14 = -9x + 36
or 9x = 22
x = 22/9 ans