Chapter 1.3-1.4 Midpoint Formula Construct Midpoints.

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Presentation transcript:

Chapter Midpoint Formula Construct Midpoints

Midpoint (of a segment) – the point that splits the segment into 2 equal parts (where the segment is cut) If X is the midpoint of AC and XC = 10, how long is AX? AC? A Z B

With Algebra Z is midpoint of MP. Find x. M Z P 3x 24 - x 3x = 24 – x +1x= + 1x 4x = 24 X = 6

Bisector (of a segment) – a line, segment ray, or plane that intersects a segment at the midpoint (it does the cutting) A Z B m bisector midpoint

Hatch Marks – short slash markings that show two or more segments are equal in length W X Y Z WX = YZ Congruent - segments that have the same measure (like equal) ~ Urkle Stephon Zack Cody

Midpoint formula:

Find the midpoint whose endpoints are (2, -3) and (-14, 13) + 2 = y midpoint + 2 = x midpoint

Find the midpoint whose endpoints are (1, -2) and (-17, 16) + 2 = x midpoint + 2 = y midpoint

What if you are missing an endpoint ? When given the midpoint and one endpoint, set up the formula just as before. (-2,2) (-3,-5) ( ?, ?)

M(-3, -5) is the midpoint of RS. If S has a coordinates (-2, 2), find the coordinates of R. (x 1, y 1 ) (-2, 2) M(-3, -5) RS + 2 = + 2 = (x 1, y 1 ) x1x1 y1y1

M(4, 2) is the midpoint of RS. If S has a coordinates (5, -2), find the coordinates of R. R (x 1, y 1 ) S (5,-2) M(4, 2) + 2 = + 2 = x1x1 y1y1 (x 1, y 1 )

Book p.41-44

The End!