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c2 chapter4

the points (-3,19), (-15,1) and (9,1) are vertices of a triangle. Show that a circle centre (-3,6) can be drawn throught the vertices of the triangle
Reply 1
Avatar for anshul95
anshul95
11
Show that the points form a right angled triangle with two of the points forming the base go on from there......
Reply 2
Avatar for steve10
steve10
7
The points do not form a right-angled triangle! They form instead an isosceles triangle. The standard way of solving this kind of problem is to show that all (three) points are equi-distant from a centre point - in this case (-3,6).
Use the distance formula to show that all three points are the same distance from the centre-point.
Reply 3
Avatar for anshul95
anshul95
11
they don't oh well thought they did if you did not know the centre you could find where the perpendicular bisectors of two different chords meet using the points given - they will always meet at the centre. This method may be better as they don't have to give you the centre point as they did in this case
(edited 13 years ago)
Reply 4
Avatar for gdunne42
gdunne42
21
tfdes
the points (-3,19), (-15,1) and (9,1) are vertices of a triangle. Show that a circle centre (-3,6) can be drawn throught the vertices of the triangle


Alternatively you could use (-3,6) as the centre of the circle and (-3,19) to find the radius of the proposed circle.
Form an equation for the circle centre (a,b) and radius = r
(x - a)^2 + (y - b)^2 = r^2
Then substitute the values to show that the other two points lie on that circle.
Reply 5
Avatar for tfdes
tfdes
OP
gdunne42
Alternatively you could use (-3,6) as the centre of the circle and (-3,19) to find the radius of the proposed circle.
Form an equation for the circle centre (a,b) and radius = r
(x - a)^2 + (y - b)^2 = r^2
Then substitute the values to show that the other two points lie on that circle.


ty..but in the book i hvnt reached the part where it teaches u to use equation of a circle..
im still on distance btween 2 points and midpoint.. so i guess i hv to use these for this question..
Reply 6
Avatar for tfdes
tfdes
OP
steve10
The points do not form a right-angled triangle! They form instead an isosceles triangle. The standard way of solving this kind of problem is to show that all (three) points are equi-distant from a centre point - in this case (-3,6).
Use the distance formula to show that all three points are the same distance from the centre-point.

yh this worked..thx

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