Name________________________
FST
9/6/12
Eqns of Lines wkst
1) How would I find the perpendicular bisector of segment AB if A(3,-1) and B(7,4)?
Step 1: Find midpoint
Step 2: Find slope of line perpendicular to the given segment.
Express the equation of the perpendicular bisector in point-slope form.
Express the equation of the perpendicular bisector in standard form.
Express the equation of the perpendicular bisector in slope-intercept form.
2) Given that A(-4,1) B(2,3) C(4,9) and D(-2,7), show that the quadrilateral is a
rhombus.
Step 1: Show that the quadrilateral is a parallelogram
a. both pairs of opposite sides are parallel
b. both pairs of opposite sides are congruent
c. 1 pair of sides is both parallel and congruent
d. diagonals bisect each other
e. both pairs of opposite angles are congruent
Step 2: Show that one pair of consecutive sides is congruent
3) ∆𝑋𝑌𝑍 has vertices X(2,-2) Y(3,1) and Z(1,9).
A) Find the equation of the median from vertex Z.
Step 1: Find the midpoint of XY
Step 2: Find the slope of the line that contains the midpoint and Z.
B) Find and equation of the altitude from Z
Step 1: Find slope of XY
4) ∆𝐴𝐵𝐶 has vertices A(-2,-1) B(0,7) and C(8,3)
A) Write equations for the 3 medians in slope intercept form.
B) Show that the three medians intersect at a single point. What is this point called?
Reminders:
To show quad is a rectangle:
1) 1st prove it is a parallelogram
a) contains one right angle
or
b) diagonals are congruent
To show a quad is a rhombus:
1) 1st prove it is a parallelogram and then prove one pair of consecutive sides
congruent
To show a quad is a rectangle:
1) Show diagonals are perpendicular bisectors of each other.