Dilations and the Equation of a Line

  • Dilations and the Equation of a Line

    David A. Yopp
    Track students’ understanding of proportional reasoning by combining transformational geometry, similar-triangle reasoning, and linear relationships.
    I recently asked a group of eighth-grade students to solve an application problem involving a runner’s distance with respect to time. The goal was to develop the equation of a line using slope and similar-triangle concepts. The Common Core State Standards for Mathematics (CCSSI 2010) suggests that middle school students might abstract the equation of a line as they repeatedly calculate slope and “check whether points are on a line through (1, 2) with slope 3” (p. 8). Additionally, the Grade 8 content standards assert that students can use similar triangles “to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane” (p. 54). I wanted to link these two Common Core recommendations in a way that makes rich connections to proportional reasoning.