Question

已知直线y=kx+b与x轴交于点P与直线y=-x+5的交点Q的纵坐标为4PQ=2√5若直线y=-x+5与x轴交于点M求S

Answer 1

解y = 0,y=kx+b,P(-b/k,0)

解y=kx+b,y=-x+5,Q((5-b)/(k+1),(5k+b)/(k+1))

解y = 0,y= -x + 5,M(5,0)

Q的纵坐标为4:(5k+b)/(k+1) = 4,k = 4-b

P(b/(b-4),0)

Q(1,4)

|PQ|² = (2√5)² = 20 = [b/(b-4) -1]² + (0-4)²

[b/(b-4) -1]² = 4

b/(b-4) -1 = ±2

b = 6或b = 2

P(3,0)或(-1,0)

(1) b = 6,P(3,0)

|PM| = |5 - 3| = 2

PM上的高为Q的纵坐标4

S⊿MPQ = (1/2)*2*4 = 4

(2) b = 2,P(-1,0)

|PM| = |5 - (-1)| = 6

PM上的高为Q的纵坐标4

S⊿MPQ = (1/2)*6*4 = 12