Question
Algebra B 1.6 Sample Work Retake
Given line AB shown in the image, which point will make a line with point C, such that this line is parallel to AB? A is (-5,1) B is (1,10) C is (1,0)
a) (5,6)
b) (-2,-2)
c) (5,5)
d) (1,-2)
Answers
GPT 3.5
To find a point that will make a line parallel to line AB, we need to find the slope of line AB first.
The slope of line AB can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
For line AB:
x1 = -5
y1 = 1
x2 = 1
y2 = 10
slope = (10 - 1) / (1 - (-5))
slope = 9 / 6
slope = 3/2
So, the slope of line AB is 3/2.
To make a line parallel to AB, it must have the same slope of 3/2.
Now, let's check each option and calculate their slopes with point C (1,0):
a) (5,6)
slope = (6 - 0) / (5 - 1) = 6 / 4 = 3/2 (same as line AB)
So, point (5,6) will make a line parallel to line AB.
b) (-2,-2)
slope = (-2 - 0) / (-2 - 1) = -2 / -3 = 2/3 (not the same as line AB)
Incorrect.
c) (5,5)
slope = (5 - 0) / (5 - 1) = 5 / 4 ≠ 3/2
Incorrect.
d) (1,-2)
slope = (-2 - 0) / (1 - 1) = -2 / 0 (undefined)
Incorrect.
Therefore, the correct answer is:
a) (5,6)
The slope of line AB can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
For line AB:
x1 = -5
y1 = 1
x2 = 1
y2 = 10
slope = (10 - 1) / (1 - (-5))
slope = 9 / 6
slope = 3/2
So, the slope of line AB is 3/2.
To make a line parallel to AB, it must have the same slope of 3/2.
Now, let's check each option and calculate their slopes with point C (1,0):
a) (5,6)
slope = (6 - 0) / (5 - 1) = 6 / 4 = 3/2 (same as line AB)
So, point (5,6) will make a line parallel to line AB.
b) (-2,-2)
slope = (-2 - 0) / (-2 - 1) = -2 / -3 = 2/3 (not the same as line AB)
Incorrect.
c) (5,5)
slope = (5 - 0) / (5 - 1) = 5 / 4 ≠ 3/2
Incorrect.
d) (1,-2)
slope = (-2 - 0) / (1 - 1) = -2 / 0 (undefined)
Incorrect.
Therefore, the correct answer is:
a) (5,6)