Question

URGENT 50 POINTS!!!!! A line passes through the points (15,−13) and (16,−11). Hollis writes the equation y+13=(x−15) to represent the line. Which answer correctly analyzes his equation?

His equation is incorrect. He incorrectly wrote the slope and switched the values of the coordinates. He should have written y−15=2(x+13).

His equation is incorrect. He switched the values of the coordinates. He should have written y−15=x+13.

His equation is correct. He correctly included and placed all parts for the point-slope form of the equation of the line.

His equation is incorrect. He switched the signs of the coordinates. He should have written y−13=x+15.

His equation is incorrect. He incorrectly wrote the slope and switched the signs of the coordinates. He should have written y−13=2(x+15).

His equation is incorrect. He incorrectly wrote the slope in his equation. He should have written y+13=2(x−15).

Answer 1

The question asks us to find the slope of the line that goes through the origin and is equidistant from the two points P=(1, 11) and Q=(7, 7). It's given that the originis one point on the requested line, so if we can find another point known to be on the line we can calculate its slope. Incredibly the midpoint of the line segment between Pand Qis also on the requested line, so all we have to do is calculate themidpoint between Pand Q! (This proof is given below).Let's call Rthe midpoint of the line segment between Pand Q. R's coordinates will just be the respective average of P's and Q's coordinates. Therefore R's x-coordinate equals 4 , the average of 1 and 7. Its y-coordinate equals 9, the averageof 11 and 7. So R=(4, 9).

Answer 2

He incorrectly wrote the slope in his equation. He should have written y+13=2(x−15).

Explanation: