A graph is given with the line going from (-2, 2) to (2,8).
a) Find the length of this line.
b) Find the midpoint of the line.
c) write an equation for this line.
my answers-
a) 2√10
b) 0,5
c) y = 1.5x + 5
please check these answers.
a) √(4^2+6^2) = √52 = 2√13
b) ok but should be (0,5)
c) y=1.5x - 5
c) my bad - you are right
y-2 = 3/2 (x+2)
y = 3/2 x + 5
To verify your answers, let's go through each question step by step:
a) Find the length of this line.
To find the length of a line, we can use the distance formula. The distance formula is given by the formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, we have the coordinates (-2, 2) and (2, 8). Plugging these values into the formula, we get:
d = √((2 - (-2))² + (8 - 2)²)
= √((4)² + (6)²)
= √(16 + 36)
= √52
= 2√13
So, the correct answer for the length of the line is 2√13, not 2√10.
b) Find the midpoint of the line.
The midpoint of a line segment is found by taking the average of the x-coordinates and the average of the y-coordinates.
In this case, the x-coordinates are -2 and 2, and the y-coordinates are 2 and 8. Taking the average, we get:
x-coordinate of the midpoint = ( -2 + 2 ) / 2 = 0 / 2 = 0
y-coordinate of the midpoint = ( 2 + 8 ) / 2 = 10 / 2 = 5
So, the midpoint of the line is (0, 5), which matches your answer.
c) Write an equation for this line.
To write an equation for a line, we can use the slope-intercept form: y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (-2, 2) and (2, 8) again, we can calculate the slope:
m = (8 - 2) / (2 - (-2))
= 6 / 4
= 3/2
Next, we need to find the y-intercept (b) using one of the given points on the line, let's say (-2, 2). We substitute the values into the slope-intercept form and solve for b:
2 = (3/2)(-2) + b
2 = -3 + b
b = 5
So, the equation for this line is y = (3/2)x + 5, not y = 1.5x + 5.
To summarize:
a) The length of the line is 2√13.
b) The midpoint of the line is (0, 5).
c) The equation for this line is y = (3/2)x + 5.