Shape
Copyright David & Cynthia Thomas, 2009
Chapter Five: Summary
Chapter Five began by asking three questions. The answers to those questions may be summarized as follows: In coordinate geometry,
· Questions #1:
o Segment length: If a segment has endpoints A(a1, a2) and B(b1, b2), the length of the segment is given by the formula .
o Segment midpoint: If a segment has endpoints A(a1, a2) and B(b1, b2), the midpoint of the segment is given by the formula .
o Slope of a line or segment: If a segment has endpoints A(a1, a2) and B(b1, b2), the slope of the segment is given by the formula .
o Parallel lines or segments: Lines and/or segments that are parallel have the same slope.
o Perpendicular lines or segments: Lines and/or segments that are perpendicular have slopes that are negative reciprocals of one another (i.e., the product of their slopes equals -1).
· Questions #2:
o Triangle area: If the coordinates of the vertices of a triangle are represented as , the area of the triangle is given by .
o Polygons area: Since every n-gon may be divided into n-2 triangles, the triangle area formula is used n-2 times to compute these areas and their sum computed.
· Question #3:
o Translations are represented using slide arrows. The differences in the x- and y-coordinates of the endpoints of the slide arrow are added to the x- and y-coordinates, respectively, of the polygon vertices to obtain the coordinates of the image of the polygon.
o Reflections are represented reflecting lines, or mirrors. Image points are located the same distance from the mirror as the object points.