1 The line l has equation 2x-y-1=0.The line M passes through the point A (0,4) and is perpendicular

题目

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

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)
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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