senoritace Posted August 30, 2011 Share Posted August 30, 2011 1)If P and Q are two points on the line 3x + 4y = -15 such that OP and OQ= 9 units, The area of triangle POQ is given by a) 18* sqrt(2) b) 3* sqrt(2) c) 6* sqrt(2) d) 15*sqrt(2) 2) The equations of two sides of isoceles triangle ABC are x+y=5 and 7x-3y=3 respectively. What will be the length of the intercept cut by the side BC on the y-axis. a) 9/5 b) 8 c) 1.5 d) no unique solution 3) A line is represented by the equation 4x + 5y = 6 in the coordinate system with origin (0,0). You are required to find the equation of the straight line perpendicular to this line that passes through the point (1,-2) [which is in the coordinate system where origin is at (-2,-2)]. a)5x-4y=11 b)5x-4y=13 c)5x-4y=-3 d)5x-4y=7 Quote Link to comment Share on other sites More sharing options...
flying2finn Posted September 5, 2011 Share Posted September 5, 2011 i am still working on the first... second ...could u tell which equation belongs to which side like x+y=5 is AB.... the third one's easy..if the new origin is at -2,-2 the point 1,-2 in the new system would originally be at -1,-4 in the old system.now all the options with the correct slope 4/5 can be verified to fit the point. A is the correct answer. Quote Link to comment Share on other sites More sharing options...
flying2finn Posted September 6, 2011 Share Posted September 6, 2011 The answer to the first question is 18* sqrt(2). It should have been mentioned that the O mentioned is the origin.Or may be i should have known that... anyway if the line is ax+by+c=0 and the point is (p,q) the shortest distance i.e.. perpendicular would be ap+bq+c/rt(a^2+b^2) Now we can get the height of the triangle 3*0 +4*0+15/rt(3^2+4^2) =3. we have the height of the triangle. The perpendicular divides the triangle into two similar triangles since it is an isosceles triangle. Take one, we know the two sides; the height and hypotenuse. The base can be calculated through a^2+b^2=c^2 where c is the hypotenuse. We get the base as 6 rt2. This is the base of only one of the triangles..since they are similar..the total base of the triangle would be 2* 6 rt2 =12 rt2 Now we have the base and height of the triangle POQ. 12 rt2 and 3 Area is 1/2 * base * height=18 rt2 Hence A is the correct answer Quote Link to comment Share on other sites More sharing options...
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