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標題:

F.4 Quadratic Equation

發問:

In a figure , y=kx(k>0) is a straisht line with points B and E lying on it. ABCD and DEFG are two squares each with one side lying on the x-axis.1. If the coordinatef of A are (2,0), find the coordinates of D in terms of k.2. Hence find the value of k if the area of the square DEFG is 225/4 square... 顯示更多 In a figure , y=kx(k>0) is a straisht line with points B and E lying on it. ABCD and DEFG are two squares each with one side lying on the x-axis. 1. If the coordinatef of A are (2,0), find the coordinates of D in terms of k. 2. Hence find the value of k if the area of the square DEFG is 225/4 square units. 3. Find the coordinates of F.

最佳解答:

1) y=kx......(*) sub x=2 into (*) y=2k AB=2k D must be a point lies on x-axis (?,0) as ABCD is a square, so AB = AD so AD=2k the coordinate of D is (2k,0) 2) the length of the side of square DEFG= √(225/4) = 15/2 units at point E, y=15/2 and x=2k as E is the point just above D Sub (2k,15/2) into (*) 15/2= k(2k) 15/4=k^2 k=√15/2 or -√15/2 3) the coordinate of F=(2k+15/2,0) or (2k+15/2,15/2) =(√15+15/2,0) or (√15+15/2,15/2) (depend F is on x-axis or not)

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