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Distance from a point to a line

Distance from a point to a line. Tuesday March 4th . Test?. When would be the best time for your chapter 2 test? Before or after march break? . Distance between a line and a point. What is the fastest way to get to the 401 from point A? . 401 hwy. Path B. Point (x, y) .

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Distance from a point to a line

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  1. Distance from a point to a line Tuesday March 4th

  2. Test? When would be the best time for your chapter 2 test? Before or after march break?

  3. Distance between a line and a point What is the fastest way to get to the 401 from point A? 401 hwy Path B Point (x, y) The shortest distance between a point and a line is a to follow a path that is perpendicular to the line

  4. Example If the Thames rives follows the line: 3x – 2y = 10, and your canoe is at the point (-1, -2), what is the shortest distance between you and the river? • Draw a picture. • Figure out the slope of your original line. • Figure out the slope of your direction line. This is the line that is perpendicular to your original line. • You now have y = mperpx + b for your direction line, but you don’t know b. Figure out b by substituting your point into the line equation. • Determine where the two lines cross by solving a system of two equations (the two lines) and two unknowns (the x, y coordinates of the point where your direction line crosses the original line. • Use your distance formula to find the distance from this crossing location and the original point.

  5. Practice in your teams If the shoreline of lake Erie follows the line: 12 – 6y = 2x Then, what is the shortest distance between a boat at (4, -7) and the shore?

  6. Practice individually • Khan academy distance from a point to a line checkpoint!

  7. Practice In your teams A triangle has the circumcenter, (-4/3, 4/3) and the verticies: A(4, 2), B(-6, 4), and C(-2, -4). • Calculate the slope of AB. • Determine the shortest distance between the circumcenter and the line AB. • Does this path from the circumcenter and the line ABintersect AB at the midpoint of this line? Check this. • Determine the distance from point A to the circumcenter. • Guess the distance from point B to the circumcenter. Check your guess. • Write an equation for the circle that just touches triangle ABC at each of its vertices

  8. Homework • Page 95 #1, 2, 5, 21 • Page 103 #5, 6, 9, 14

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