Question

Show that the points (4,1) is the centre of the circle on whose circumference lie the points (-2,9),(10,-7) and (12,-5).​

Answer 1

Answer:

As we all know the line from the centre of a circle to any point in the circumference of the circle is the radius of the circle

Therefore Let O be the centre of the circle with coordinates (4,1). And A(-2,9), B(10,-7) and C (12,-5) be the points on the circumference of the circle.

To show that (4,1) is the centre of the circle we need to prove that AO=BO=CO.

Using Distance Formula - ✓(x2-x1)²+(y2-y1)²

AO = ✓(-2-4)²+(9-1)²

= ✓(-6)²+(8)²

= -6+8

= +2

BO = ✓(10-4)²+(-7-1)²

= ✓(6)²+(-8)²

= 6-8

= -2

CO = ✓(12-4)²+(-5-1)²

= ✓(8)²+(-6)²

= 8-6

= +2

Since AO=BO=CO , We prove that (4,1) is in the centre of the circle which has the points(-2,9),(10,-7) and (12,-5) in it's circumference