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A triangle shows points A(2,8), B(14,4) and C(4,2). M is the midpoint of AC.

a. Write down the coordinates of M
b. Calculate the gradient of line AB.
c. Find the equation of the line parallel to AB that passes through My.

(a) M = (A+C)/2 for each coordinate - this gives (h,k)

(b) m = (4-8)/(14-2)
(c) you have a point (h,k) and a slope m, so use the point-slope form of the equation
y-k = m(x-h)

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Did you know?

Did you know that in a triangle with points A(2,8), B(14,4), and C(4,2), the midpoint of AC can be found by taking the average of the x-coordinates and the average of the y-coordinates? In this case, the midpoint M has coordinates (3,5). Furthermore, did you know that the gradient (or slope) of line AB can be calculated by using the formula (change in y)/(change in x)? By substituting the coordinates of points A and B into this formula, we find that the gradient of line AB is -4/6 or -2/3. Lastly, did you know that a line parallel to AB and passing through M can be found by using the equation y-y1 = m(x-x1), where m represents the gradient and (x1, y1) are the coordinates of the midpoint M? Substituting the values of M (3,5) and the gradient of AB (-2/3) into this equation, we can find the equation of the line.