1.Given 3 points X(-2,2), O(1,y), Y(4,10). If OX=OY, find the value of y.
2.Find the coordinates of Q at which the line segment ST cuts the y-axis, where the coordinates of S and T are (-4,-1) and (2,3) respectively.
3. Given that tanx=3/4, evaluate 3sinx-4cosx/3sinx+4cosx.
maths
2008-07-09 11:48 pm
回答 (1)
2008-07-10 12:14 am
✔ 最佳答案
1 ∵OX=OY∴√[(-2-1)2+(2-y)2]=√[(4-1)2+(10-y)2]
9+(4-4y+y2)=9+(100-20y+y2)
16y=96
y=6
2 ST equation:
(-1-3)/(-4-2)=(-1-y)/(-4-x)
2/3=(-1-y)/(-4-x)
2(-4-x)=3(-1-y)
-8-2x=-3-3y
2x-3y+5=0_________________(*)
∵the line segment ST cuts the y-axis
∴Let Q coordinates be (0,y).
put Q into (*),
-3y=-5
y=5/3
∴Q coordinates=(0,5/3).
3. 3sinx-4cosx/3sinx+4cosx
=(3tanx-4)/(3tanx+4)
=[3(3/4)-4]/[3(3/4)+4]
=-7/25
收錄日期: 2021-04-23 20:37:13
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