Combination Lock

 

The LOCK is made up of a series of 6 numbers, based on the answers to the following questions. The input for the lock is "{3rd, 4th, 2nd, 1st, 5th, 6th}". From our inside informant, we know that the answers for the following questions must first be put in order from largest (1st) to smallest (6th) and then entered in the specific pattern above. Luckily there is no security triggers on this LOCK so if you get it wrong you can just start over again. Good luck.

​

The following questions will give you a set of ordered pairs for each question. You will take each value of the ordered pair and line them up accordingly. 

For example, if you get (1,4), (10,3), and (2, 12) as answers to the questions you would then put them in descending order, 12, 10, 4, 3, 2 and then match the specific order that you received from the informant. 

​

​

Question 1: 

What would be the midpoint of a line segment with endpoints (150,15) and (8,17)?

​

Question 2:

A triangle has vertices A(-5,4), B(4,4), and C(4,13). Find the coordinates of the point of intersection of the median from A to BC and the altitude from B to AC. Express your answer as an ordered pair.

​

​

Question 3:

Three vertices of a parallelogram ABCD are A(8,9), B(2,8), and C(4,1). Find the fourth vertex. Express your answer as an ordered pair.

​

​

​