solved examples geometry

Question: Find the centroid of the triangle whose sides are x + y - 1 = 0, x - 3y + 3 = 0 and x - y - 1 = 0. Answer: Let AB represent the side x + y - 1 = 0 ...(i) Let BC represent the side x - 3y + 3 = 0 ... (ii) Let CA represent the side x - y - 1 = 0 ... (iii) Solving (i) a..

Question 1 - Question: Find the centroid of the triangle whose sides are x + y - 1 = 0, x - 3y + 3 = 0 and x - y - 1 = 0. Answer: Let AB represent the side x + y - 1 = 0 ...(i) Let BC represent the side x - 3y + 3 = 0 ... (ii) Let CA represent the side x - y - 1 = 0 ... (iii) Solving (i) ..

Question: Solve the following equation: 5x-(3x-1)=x-4 Answer: 5x-(3x-1)=x-4 5x-3x+1=x-4 2x-x=-4-1 x=-..

Then (x 1 , y 1 ) lies on both (i) and (ii). Solving for x 1 and y 1 by the method of cross multiplication, we obtain ..

Question: Answer: Line through the origin and perpendicular to x + y - 4 = 0 is x - y = 0 ...(iv) \ The foot of the perpendicular is given by solving (i) and (iv), x = y = 2. (2,2) are the coordinates of the foot of the perpendicular. Line through the origin perpendicu..

Question: Solve the inequation and graph the solution set on the number line. Answer: ..

Question: Solve the following equation: Answer: ..

Question: Solve the following equation: Answer: 5(3x+5) = 2(2x-1) (by cross-multiplication) 15x-4x = -2-25 11x = -27 ..

Question: Show that the lines 3x - y - 6 = 0, 4x - y - 7 = 0 and 2x - y - 5 = 0 are concurrent. Answer: Given lines are Solving (i) and (ii) for x and y, we get The point of intersection is (1,-3). Now substituting x = 1 and y = -3 in the LHS of (iii), we get \ The thr..

Solving (ii) and (i) for h and k, we have Reflection of P (-1,1) about the line 3x + 4y = 32 ..