To construct a line perpendicular to a given line through a point on that given line, we first create a line segment that has the given point as the midpoint.[br][br]1) Using the Circle with Center through Point tool [icon]/images/ggb/toolbar/mode_circle2.png[/icon], create a circle with a center at P and any radius.[br]2) Mark the points where the circle intersections the line using the Intersect tool[icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon]. [br]3) Now you can use what you know to create a perpendicular line through the original point, which is the midpoint between the two intersection points.[br]4) Verify that the new line is perpendicular to the original by using the Angle Measure tool[icon]https://www.geogebra.org/images/ggb/toolbar/mode_angle.png[/icon].