# Thread: Co-ordinate Geometery urgent help needed

1. ## Co-ordinate Geometery urgent help needed

A, B, C and D are (-7,4), (3,-1), (6,1) and (k,-15) respectively.

1] Find the gradient of AB
2] Find the equation of AB and simplify the answer
3] Find the length of AB
4] The point E is the mid-point of AB. Find the co-ordinates of E.
5] CD is perpendicular to AB. Find the value of k in D.

For question 1 I used y2-y1 over x2-x1 to get the gradient which I think is -6,

For question 2 I then used formula of a line and continued:

y - y1 = m (x - x1)
y - 4 = -6 (x + 7)
y - 4 = -6x - 42
y + 6x + 38 = 0

For question 3 I worked the length of AB to be:

√ (x2-x1)² + (y2-y1)²
√ (3 + 7)² + (-1 + 7)²
√ 10² + 6² [100 = 36]
AB = √136

I'm really concerned this is wrong and I don't know how to do the rest of the question. Can someone please help me?

2. Originally Posted by db5vry
A, B, C and D are (-7,4), (3,-1), (6,1) and (k,-15) respectively.

1] Find the gradient of AB
2] Find the equation of AB and simplify the answer
3] Find the length of AB
4] The point E is the mid-point of AB. Find the co-ordinates of E.
5] CD is perpendicular to AB. Find the value of k in D.

For question 1 I used y2-y1 over x2-x1 to get the gradient which I think is -6,

For question 2 I then used formula of a line and continued:

y - y1 = m (x - x1)
y - 4 = -6 (x + 7)
y - 4 = -6x - 42
y + 6x + 38 = 0

For question 3 I worked the length of AB to be:

√ (x2-x1)² + (y2-y1)²
√ (3 + 7)² + (-1 + 7)²
√ 10² + 6² [100 = 36]
AB = √136

I'm really concerned this is wrong and I don't know how to do the rest of the question. Can someone please help me?
1/ is wrong,

$\frac{y_2-y_1}{x_2-x_1}$= $\frac{-1-4}{3+7}$

$\frac{-5}{10}$ $=-\frac{1}{2}$

2/ i get $-\frac{1}{2}x+\frac{1}{2}$ you already have the slope which is $-\frac{1}{2}$ plug in the other numbers to $y=-\frac{1}{2}x+b$ and solve for b

3/ the value of y1 is 4 and you used 7 which is wrong
answer should be $\sqrt{125}$= $11.18$

4/

$M= (\frac{x_1+x_2}{2} + \frac{y_1+y_2}{2})$= $(\frac{-7+3}{2} + \frac{4-1}{2})$

$=(\frac{-4}{2} + \frac{3}{2})$ $=(-2,1/2)$