The gradient of AB is -2, it just doesn’t show due to formatting issues.
Hi @Kieran, that is correct, the gradient of line AB is equal to -2.
Line AB: y = mx + c
m = (-7-9)/(10-2) = -2
In order to find c we can substitute the coordinates of one of the points belonging to the line into the equation:
A (2,9): 9 = -2*2 + c
c = 13
Final equation of the line AB: y = -2x + 13
Next we can find the equation of line AC:
As we know, lines AB and AC are perpendicular, which means their gradients are reciprocal and have opposite signs:
NB: the reciprocal is the inverse value of a number, for example the reciprocal of number n is 1/n. The reciprocal number of 2 is 1/2, or 0.5.
Line AC: y = 0.5x + c
To find the y-intercept, c, we can again substitute the coordinates of a point that belongs to the line AC, which is A (2,9):
9 = 0.5*2 + c
c = 8
Equation of the line AC: y = 0.5x + 8
Lastly, we need to find the y-coordinate of point C. We will do that by substituting 6 for x in the equation of the line AC:
y = 0.5*6 + 8 = 11
k = 11
hi Kieran
you have correctly found the gradient of line AB = -2
We know that line AC is perpendicular to line AB therefore the gradient of line AC is -1/2
we also know that a point on line AC is (2,9)
So we can now work out what k is (6,k) by substituting x=6 into the equation
1/2 x 6 + 8 = 3 + 8 = 11
here is an image of the graph
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