Answer:
Your family takes out a mortgage and buys a new house. - Invesment
When a household purchases a new house, it is considered an investment according to macroeconomic theory.
You use your $200 paycheck to buy stock in AT&T. - Investment.
Stock is a form of capital because it is bought with the expectation of getting a return. Buying stock is a form of investment.
Your roommate earns $100 and deposits it in his account at a bank. - Saving.
Your roommate does not need the $100 to pay for his daily expenses, and instead, saves that money at the bank. It is a form of saving as the name of the transaction implies.
You borrow $1,000 from a bank to buy a car to use in your pizza delivery business. - Investment.
You are borrowing to buy a car because you feel the car will provide you economic benefits in the future. Thus, the car is a capital asset, and a form of investment.