Quadrilateral 2

Show that the quadrilateral with vertices P1(0,1), P2(4,2), P3(3,6) P4(-5,4) has two right triangles.

Correct answer:

x =  2

Step-by-step explanation:

x1=0 y1=1 x2=4 y2=2 x3=3 y3=6 x4=5 y4=4 a=(x1x2)2+(y1y2)2=(04)2+(12)2=174.1231 b=(x2x3)2+(y2y3)2=(43)2+(26)2=174.1231 c=(x3x4)2+(y3y4)2=(3(5))2+(64)2=2 178.2462 d=(x4x1)2+(y4y1)2=((5)0)2+(41)2=345.831 u1=(x1x3)2+(y1y3)2=(03)2+(16)2=345.831 u2=(x2x4)2+(y2y4)2=(4(5))2+(24)2=859.2195 t1=u12a2b2=5.83124.123124.12312=0 t2=u22b2c2=9.219524.123128.246222.5581013 t3=u12c2d2=5.83128.246225.8312=68 t4=u22d2a2=9.219525.83124.12312=34 t1=0 => P1P2P3 = 90° t2=0 => P2P3P4 = 90° x=2 angles=2

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