1 The line l has equation 2x-y-1=0. The line M passes through the point A (0,4) and is perpendicular to the line l.
(a) Find an equation of m and show that the lines l and m intersect at the point P (2,3).the line n passes through the point B(3,0) and is parallel to m.
(b) Find an equation of n and hence find the coordinates of the point Q where the lines L and n intersect.
(c) Prove that AP =BQ=PQ.
2 A,B and C are the points (0,2) (5,7)and(12,0)respectively.
(1) find the lengths AB,BC and CA of the sides of the triangle ABC, and show that AB^2+BC^2=CA^2.
Deduce the size of angle ABC
最好有简单的步骤
參考答案:(a)因为L的斜率为2，而M与L垂直，所以M的斜率为－1/2，而M又经过点（0,4），所以M的方程为y＝(－1/2)*X+4
联立方程组：y＝(－1/2)*X+4
2x-y-1=0 即可解得L和M相交于(2,3).
（b)
题目其实很简单，我帮你翻译下，你自己做吧，因为很难打字，又实在太简单了！
1 The line l has equation 2x-y-1=0. The line M passes through the point A (0,4) and is perpendicular to the line l. 意为：直线L的方程为2x-y-1=0，直线M经过点A (0,4)且和直线L垂直。
(a) Find an equation of m and show that the lines l and m intersect at the point P (2,3).the line n passes through the point B(3,0) and is parallel to m. 意为：找出L的方程以证明L和M相交于P (2,3).直线N经过B(3,0)且和M平行。
(b) Find an equation of n and hence find the coordinates of the point Q where the lines L and n intersect.
找出N的方程，并找出L和N的交点Q
(c) Prove that AP =BQ=PQ. 证明 AP =BQ=PQ
2 A,B and C are the points (0,2) (5,7)and(12,0)respectively.
A,B and C分别是点(0,2) (5,7)and(12,0)
(1) find the lengths AB,BC and CA of the sides of the triangle ABC, and show that AB^2+BC^2=CA^2.
Deduce the size of angle ABC
找出三角形ABC的三边，并证明AB^2+BC^2=CA^2
推出角ABC的度数
