Question

1. the points given are two of the 3 vertices of a right triangle. Which could be the third vertex of the triangle given 2 points are (-4,-5) & (3,2) ?

2.) A circle with center O and radius r is intersected at 2 distinct points by line l. Which is true?

a. The distance between the points of intersection is less than r

b.There is at least 1 point on l whose distance from O is less than r

c. There is no point on l whose distance from O is less than 1/2


3.) In triangle ABC, the measure of A is = the measure of C. If the length of AB is x, the length of AC is x-2, and the length of BC is 3x-8, what is the length of AC?
Answer? 5

Answer 1

#1
If you make a sketch and assume the two points form the hypotenuse, then it should be easy to see the third point could be
(3,-5) or (-4,2)

#2
give yourself an actual circle with a radius
e.g. r = 10
Draw in different lines and test each case
Make sure your consider the case when your line is a diameter.
in c) did you mean " .... from O is less than 1/2r" ?

#3. your triangle is isosceles with AB = BC, so
3x-8 = x
2x = 8
x = 4
then AC = 4-2 = 2