Combining the knowledge and skills of finding midpoints, gradients of perpendicular lines, and equation of straight lines, we can now find the equation of the perpendicular bisector of a line segment AB.[br][br][table][tr][td][b]Step 1:[/b][/td][td]Find the gradient of line [math]AB[/math][/td][/tr][tr][td][b]Step 2:[/b][/td][td]Find the gradient of line [math]\perp AB[/math] using [math]m_1\times m_2=-1[/math][/td][/tr][tr][td][b]Step 3:[/b][/td][td]Find the midpoint of [math]AB[/math].[/td][/tr][tr][td][b]Step 4:[/b][/td][td]With midpt [math]AB[/math] and [math]m_{\perp AB}[/math], find the equation of the line using [math]y-y_1=m\left(x-x_1\right)[/math].[/td][/tr][/table][br][b]Key feature of perpendicular bisector:[/b] Any point along the perpendicular bisector of AB is [b]equidistant[/b] from A and B.[br][br]You may use the applet below to guide your thinking and working process. Afterwhich, you may wish to attempt on your own with a new question.