What is the equation of the straight line perpendicular to the midpoint of the straight line that passes through (0,5) and (-4,7)?
Firstly, it's important to note that the question concerns straight lines, so it will be possible to express the answer in the form y=mx+c where m is the gradient and c is the y-intercept.To start, we need to the find the gradient. We can find the gradient of the line passing through the given points by using the difference in y divided by the difference in x:(5-7)/(0--4) = -2/4 = -1/2The line perpendicular to this line will have the gradient -1/m, ie. -1/(-1/2) = -1 * (2/-1) = 2 so m in our line is 2.Now we have the gradient, we need to find the midpoint of the points so that we have the coordinates of a point through which our line passes.(((0+-4)/2),((5+7)/2)) or (-2,6)We can now plug these coordinates (x=-2, y=6) and the gradient (m=2) into the equation of a straight line, y-y1 = m(x-x1):y-6 = 2(x--2)y-6 = 2x + 4y = 2x + 10
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