Coordinate geometry help :( (1 Viewer)

[JasonNg]

1.
(a) Show that the point (-7,7) lies on the line joining A(-2,0) and B(3,-7).
(b) Find the ratio in which the point divides AB.

2. Find the coordinates of the centre of a circle that passes through points (7,2), (2,3) and (-4,-1).

For question 1, i already found (a) but don't know how to find (b).

And for question 2, i'm just completely lost. Haha. Any help would be appreciated. You can post up the whole solution or just give me some guidance on how to approach this question (like a hint).

Thanks Guys!

 

[Internet_Police]

1b.

Is fairly standard interval division question.

Usually they give you two points, a ratio and ask you find the third point. This time they give you all these points and ask for the ratio.

2. Can most likely be done just by drawing a picture (plot the three points and then use common sense).

 

[AAEldar]

For 2, let A(7, 2), B(2, 3) and C(-4, 1).

Find the equations of the line AB and BC (and hence the gradient). Then find the equations of the lines that are PERPENDICULAR to these lines AND pass through the midpoints of each of them. Solve these 2 perpendicular lines simultaneously and you'll come up with the centre of the circle.

Finding the radius is then easy, you just find the distance between one of the points and the centre.

Hopefully that makes sense. Draw a picture for yourself and it should be easier to see.

 

[Carrotsticks]

Alternatively you could let the centre of the circle be K (x,y).

AK = BK yields one equation in terms of x and y.

BK = CK yields another equation.

Solve simultaneously for x and y.