Let Px1, y1 lie on y=3x, theny1=3x1P=x1, 3x1Let Qx2, y2 lie on 2y+x=2, then2y2+x2=2x2=2-2y2Q=2-2y2, y2It is given that midpoint of PQ=2,3By midpoint formula, midpoint of PQ, R=x1+x22, y1+y22=2,3x1+2-2y22, 3x1+y22=2,3Comapringx1+2-2y22=2x1+2-2y2=4x1-2y2=2 ________13x1+y22=33x1+y2=6 ______________2Multiply equation 2 by 2 and add to 1x1+6x1-2y2+2y2=2+127x1=14x1=2Put in equation 12-2y2=22y2=0y2=0P=2,6Q=2,0PQ=2-22+6-02=36=6The given answer in wrong

Question 3 plz

Question 3 plz The 'n centre of the triangle formed by the axes and the tine Let •P' bea point on the l.ney= 3x and Q lies on 2y and the mid-point ofPQ (2.2), tne [Ans. PQ = 41 The co-ordinates of the middle points of the sides of a triangle are (4. 2), (3. 3) and (2. 2). then the co-ordinates of its centroid are 7/3) (D) none of these c. A straight line through the pointA (1. 1) meets the parallel lines4x 2y = 9 & 2x + y +6: O at points F and Q respectively, Then the point A divides the segment PQ in the ratio _ The co—ordinates cf the orthocentre of the triangle bounded by the lines. 4 x — 7 y • 10 = O: x + y = 5 and 7 x +4 y = 15 is: (1.2) (D) (1.-2) The vertices ofa A ABC are B(7, 6) and C(5, —4) . Then: measure of angle B IS ,'t/4 equation of the altitude drawn from the vertex C has the equation, 3X+2y —7 - O

L e t P (x_{1}, y_{1}) l i e o n y = 3 x, t h e n y_{1} = 3 x_{1} P = (x_{1}, 3 x_{1}) L e t Q (x_{2}, y_{2}) l i e o n 2 y + x = 2, t h e n 2 y_{2} + x_{2} = 2 x_{2} = 2 - 2 y_{2} Q = (2 - 2 y_{2}, y_{2}) I t i s g i v e n t h a t m i d p o i n t o f P Q = (2, 3) B y m i d p o i n t f o r m u l a, m i d p o i n t o f P Q, R = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) = (2, 3) (\frac{x_{1} + 2 - 2 y_{2}}{2}, \frac{3 x_{1} + y_{2}}{2}) = (2, 3) C o m a p r i n g \frac{x_{1} + 2 - 2 y_{2}}{2} = 2 x_{1} + 2 - 2 y_{2} = 4 x_{1} - 2 y_{2} = 2________(1) \frac{3 x_{1} + y_{2}}{2} = 3 3 x_{1} + y_{2} = 6______________(2) M u l t i p l y e q u a t i o n (2) b y 2 a n d a d d t o 1 x_{1} + 6 x_{1} - 2 y_{2} + 2 y_{2} = 2 + 12 7 x_{1} = 14 x_{1} = 2 P u t i n e q u a t i o n 1 2 - 2 y_{2} = 2 2 y_{2} = 0 y_{2} = 0 P = (2, 6) Q = (2, 0) P Q = \sqrt{{(2 - 2)}^{2} + {(6 - 0)}^{2}} = \sqrt{36} = 6 T h e g i v e n a n s w e r i n w r o n g

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