MPM2D Name: ______________

VERIFYING GEOMETRIC PROPERTIES

1. Points P(1,8), Q(9,2) are endpoints of a diameter of a circle and R(8,9) is another point on the same circle.
  1. Find the coordinates of the centre of the circle.
  2. Show V PQR is a right angled triangle.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. Given a quadrilateral with vertices S(-3,4), T(1,2)., U(3,-4) and V(-5,-2), prove that the midsegments of the quadrilateral form a parallelogram.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
  1. A circle is defined by x2+y2=25. On the circumference of the circle lie points A(-3,4), B(4,3), C(3,-4) and D(-4,3). Verify algebraically that the quadrilateral formed by joining all four points is a square.

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  2. Triangle ABC is formed using A(0,0), B(0,5), C(4,0). Squares are drawn on the outside of each leg of the triangle. The lines through D and C and through B and F intersect at H. Show that AH is perpendicular to BC.

 
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