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Mathematicians - Help Please!!!!

Coordinate geometry. :s-smilie:

1) Given that the straight line passing through the points A(2,-3) and B(7,K) has gradient 3/2...

a) find the value of k.
b) show that the perpendicular bisector of AB has the equation 8x+12y-45 = 0.

2) The verticles of a triangle are the points A(5,4), B(-5,8)
and C(1,11)..

a) Find the equation of the straight line passing through A and B, giving your answer in the form ax+by+c = 0.
b) Find the coordinates of the point M, the mid-point of AC.

thanks in advance.

Reply 1

insparato

1) Given that the straight line passing through the points A(2,-3) and B(7,K) has gradient 3/2...

Use the equation

Unparseable latex formula:

\tex \large M = \frac{Y_1 - Y_2}{X_1 - X_2}

where m = gradient and the coordinates (x1,y1) and (x2,y2)

b)show that the perpendicular bisector of AB has the equation 8x+12y-45 = 0.

Find the midpoint of the line AB using the equation

Unparseable latex formula:

\tex \large Midpoint = (\frac{x1+x2}{2},\frac{y1+y2}{2})

Then find the perpendicular gradient and use the equation

y - y_1 = m(x-x_1)

Theres the first questions hints

2) The verticles of a triangle are the points A(5,4), B(-5,8)
and C(1,11)..

a) Find the equation of the straight line passing through A and B, giving your answer in the form ax+by+c = 0.
Find the gradient between A and B using

Unparseable latex formula:

\tex \large M = \frac{Y_1 - Y_2}{X_1 - X_2}

then use the equation