a) A(5,7) and B(3,9) b) E( 1, 4) and F( 2,8) 2) find the equation of the line, in the form y=mx+b, that goes through the points: y = mx + b

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Katherine Barnett
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1 .1 medians DO IT NOW.1 Median of a Triangle 1) Determine the coordinates of the midpoint of the line segment defined by each pair of endpoints: a) A(5,7) and B(3,9) b) E( 1, 4) and F(,8) ) find the equation of the line, in the form y=mx+b, that goes through the points: A( 1,7) and B(,4) Don't Forget: y = mx + b is the equation of a straight line 'x' and 'y' represent the coordinates of all points on the line 'm' is the slope of the line 'b' is the y intercept of the line 1a) Midpoint of A(5,7) and B(3,9) x1 + x y1 + y m = y y 1 x x 1 ) find the equation of the line, in the form y=mx+b, that goes through the points: A( 1,7) and B(,4) b) Midpoint of E( 1, 4) and F(,8) 1

2 .1 medians What's New Today? Medians Median: Line segment joining a vertex of a triangle to the midpoint of the opposite side Find the equation of the median of a triangle A Median Midpoint of AB C B vertex B for triangle A (0,) B(6,6) C(8, ) vertex B for triangle A (0,) B(6,6) C(8, ) vertex B: 1) Midpoint of line AC ) slope of median B(6,6) 1) Midpoint of AC x 1 + x y 1 + y mid of AC A(0,) C(8, )

3 .1 medians vertex B for triangle A (0,) B(6,6) C(8, ) ) slope of the median vertex B for triangle A (0,) B(6,6) C(8, ) 3) y intercept of the median m = y y 1 x x 1 Note: to find the slope of the median, you must use the two points that the median connects vertex B for triangle A (0,) B(6,6) C(8, ) An equation for the median from vertex B is: Example : Find the equation of the median from vertex C for triangle A (0,) B(6,6) C(8, ) vertex C: 1) Midpoint of line AB ) slope of median Make a rough sketch: Note: only plug in values for 'm' and 'b' NOT 'x' and 'y' for the final equation of the line 3

4 .1 medians Example : Find the equation of the median from vertex C for triangle A (0,) B(6,6) C(8, ) Example : Find the equation of the median from vertex C for triangle A (0,) B(6,6) C(8, ) 1) Midpoint of AB x 1 + x y 1 + y ) slope of the median m = y y 1 x x 1 Example : Find the equation of the median from vertex C for triangle A (0,) B(6,6) C(8, ) 3) y intercept of the median Example : Find the equation of the median from vertex C for triangle A (0,) B(6,6) C(8, ) An equation for the median from vertex C is: Note: only plug in values for 'm' and 'b' NOT 'x' and 'y' for the final equation of the line 4

5 .1 medians vertices A(4,4), B( 6,), and C(,0) vertex A: 1) Midpoint of line BC ) slope of median vertices A(4,4), B( 6,), and C(,0) 1) Midpoint of BC x 1 + x y 1 + y Make a rough sketch: vertices A(4,4), B( 6,), and C(,0) ) slope of the median vertices A(4,4), B( 6,), and C(,0) 3) y intercept of the median 5

6 .1 medians vertices A(4,4), B( 6,), and C(,0) An equation for the median from vertex A is: median from vertex C for the triangle with vertices C(5,), A( 3,3), and B(, 5) vertex C: 1) Midpoint of line AB ) slope of median Make a rough sketch: Note: only plug in values for 'm' and 'b' NOT 'x' and 'y' for the final equation of the line C(5,), A( 3,3), and B(, 5) 1) Midpoint of AB x 1 + x y 1 + y C(5,), A( 3,3), and B(, 5) ) slope of the median C(5,) D( 1/, 1) x1 y1 x y m = rise run = y y 1 x x 1 6

7 .1 medians C(5,), A( 3,3), and B(, 5) 3) Determine the y intercept C(5,), A( 3,3), and B(, 5) An equation for the median from vertex C is: Homework: Complete Worksheet 7

GEOMETRY HONORS COORDINATE GEOMETRY PACKET

GEOMETRY HONORS COORDINATE GEOMETRY PACKET Name Period 1 Day 1 - Directed Line Segments DO NOW Distance formula 1 2 1 2 2 2 D x x y y Midpoint formula x x, y y 2 2 M 1 2 1 2 Slope formula y y m x x 2 1