1.The midpoint of SM is (5 -11) one endpoint is S (3,5). What are the coordinates of endpoint M?

2.Describe a process you would use to create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass.

3. How is constructing a perpendicular bisector similar to constructing an angle bisector? how is it different?

in x 3 ---> 5 ---> 7 up 2

in y 5 --> -11 --> -27 down 16
so
(7 , -27)

Hey, check any old geometry text

swing compass from each end with radius around 3/4 of your segment length
connect the two points where the circles cross.

LOL, you swing the compaas twice along each side for the angle bisector. (at the intersection you get two for one)

Like I said, just Google this or look at ANY geometry book.

http://www.mathopenref.com/constbisectline.html

http://strader.cehd.tamu.edu/geometry/bisectangle1.0/bisectangle.html

thanks

1. To find the coordinates of endpoint M, we can use the formula for the midpoint of a line segment. The midpoint formula is (x1+x2)/2, (y1+y2)/2. Given that the midpoint of SM is (5, -11) and one endpoint is S(3,5), we can substitute these values into the formula:

(x1+x2)/2 = 5
(3+x2)/2 = 5 (Substituting the x-coordinate of S(3,5) for x1 and the x-coordinate of the midpoint for x2)
3+x2 = 10 (Multiplying both sides by 2 to remove the fraction)
x2 = 10-3 (Subtracting 3 from both sides)
x2 = 7

Similarly, we can calculate the y-coordinate:

(y1+y2)/2 = -11
(5+y2)/2 = -11 (Substituting the y-coordinate of S(3,5) for y1 and the y-coordinate of the midpoint for y2)
5+y2 = -22 (Multiplying both sides by 2 to remove the fraction)
y2 = -22-5 (Subtracting 5 from both sides)
y2 = -27

Therefore, the coordinates of endpoint M are (7, -27).

2. To create the perpendicular bisector to the segment AB using only an unmarked straightedge and an unmarked compass, follow these steps:

Step 1: Draw segment AB using the straightedge. This will be the line segment that you want to bisect perpendicularly.

Step 2: Place the compass at point A and draw arcs on both sides of the line segment AB. Keep the compass radius wider than half the length of AB.

Step 3: Without changing the compass width, place the compass at point B and draw two arcs that intersect the previous arcs drawn in Step 2. These new arcs should intersect each other.

Step 4: Using the straightedge, draw a line that connects the intersection points of the arcs, creating a straight line that intersects AB at a perpendicular angle. This line is the perpendicular bisector.

3. Constructing a perpendicular bisector and an angle bisector have similarities and differences.

Similarities:
- Both constructions involve the use of a straightedge and a compass.
- Both constructions involve bisecting a given line segment or angle to divide it into two equal parts.
- Both constructions require creating congruent angles.

Differences:
- A perpendicular bisector divides a line segment into two equal halves, making the new line perpendicular to the original segment. An angle bisector, on the other hand, divides an angle into two equal angles.
- To construct a perpendicular bisector, you need to create arcs and determine the intersection points to draw the bisecting line. For an angle bisector, you also need to create arcs, but the bisecting line is drawn by connecting the vertex of the angle with an arc intersection point and extending it.
- The construction process for a perpendicular bisector is more straightforward, whereas constructing an angle bisector requires additional steps to form the bisecting line.