Writing Equations of Lines and Midpoint
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1 Writing Equations of Lines and Midpoint MGSE9 12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Aug 15 6:17 PM What am I learning today? How to write equations of lines given specific conditions How will I show that I learned it? Write the equation of a line in slope intercept form that satisfies a set of conditions Aug 15 6:19 PM 1
2 Three forms for linear equations Standard: ax + by = c Slope Intercept: y = mx + b Point Slope: y y 1 = m(x x 1 ) Nov 8 11:37 AM To write the equation of a line, you must be given one of the following sets of information: 1) The slope and the y intercept 2) The slope and a point on the line 3) Two points on the line Aug 14 6:54 PM 2
3 GIVEN SLOPE AND Y INTERCEPT Plug m and b in to slope intercept form Write an equation for each of the following lines: slope of, y intercept of 7 y intercept of 4, slope of Aug 14 6:57 PM GIVEN SLOPE AND ANY POINT ON THE LINE Point Slope Form: Using point slope form: 1) Plug in slope for m 2) Plug in point for (x 1, y 1 ) 3) Solve for y Aug 14 7:11 PM 3
4 passes through (2, 3) with a slope of Nov 10 10:43 AM passes through ( 3, 4) with a slope of Nov 10 10:44 AM 4
5 passes through (5, 6) with a slope of Nov 10 10:45 AM GIVEN TWO POINTS ON THE LINE Steps: 1) Use the given points to find the slope 2) Plug in either point, along with the slope from step 1, into the point slope form 3) Solve for y Aug 17 7:57 AM 5
6 passes through ( 2, 1) and (3, 4) Nov 10 10:48 AM passes through (1, 5) and (4, 2) Aug 17 8:00 AM 6
7 passes through (3, 0) and ( 3, 1) Aug 17 8:00 AM passes through (2, 5) and ( 3, 5) Aug 17 8:00 AM 7
8 passes through (3, 7) and (3, 1) Aug 17 8:00 AM Two lines are PARALLEL if they lie in the same plane and never intersect In order for two lines to never intersect, then they must be "rising" and "running" at the exact same rate. Therefore, if two lines have equal slopes, then they will be parallel. Aug 11 6:07 PM 8
9 Two lines are PERPENDICULAR if they intersect to form a right angle In order for two lines to intersect at a 90 o angle, as one is "rising", then the other is "running" at the same rate, and vice versa. However, the directions in which they are moving will be different. Therefore, if two lines have slopes that are negative reciprocals of each other, then they will be perpendicular. Nov 10 10:54 AM Determine which of the lines, if any, are parallel, and which are perpendicular line a: through ( 4, 1) and ( 6, 7) line b: through ( 7, 5) and (1, 11) line c: through (2, 5) and (4, 9) line d: through (4, 3) and (10, 5) Feb 2 4:04 PM 9
10 passes through (2, 3) and is perpendicular to the line Nov 10 10:56 AM passes through ( 3, 4) and is parallel to Oct 22 11:09 PM 10
11 passes through (5, 6) and is parallel to Oct 22 11:11 PM passes through (3, 5) and is perpendicular to the line through (1, 4) and (3, 2) Oct 22 11:15 PM 11
12 In ABC, A( 3, 4), B(5, 2), and C( 4, 5). Write the equation of the altitude to AB. Nov 11 5:30 AM How can we find the point that divides a segment in half? Formula: Oct 27 9:33 PM 12
13 Find the coordinate of the point that is ½ of the way from A to B A B A B Oct 27 9:33 PM THE MIDPOINT FORMULA Given two points, A(x 1, y 1 ) and B(x 2, y 2 ), the MIDPOINT of AB can be found using the formula: Sep 20 7:59 AM 13
14 Find the coordinates of the midpoint of AB B A Sep 20 8:04 AM If the midpoint of AB falls at (7, 9), and point A is located at ( 2, 4), then find the coordinates of B Sep 20 8:07 AM 14
15 In ABC, A( 3, 2), B(9, 4), and C(5, 12). Write the equation of the median from C. Nov 11 5:30 AM In ABC, A( 6, 2), B(8, 4), and C(18, 12). Write the equation of the midsegment that is parallel to BC. Nov 11 5:30 AM 15
16 In ABC, A(2, 3), B(12, 5), and C(9, 8). Write the equation of the perpendicular bisector of AB. Nov 11 5:30 AM Homework: Writing Equations of Lines WS Nov 5 11:23 AM 16
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