Answer:5/3 + 2/4 = 13 /6 = 2 1 /6 ≅ 2.1666667
Step-by-step explanation:
What is an equation of the line that passes through the point (-1, 4) and is parallel
1 answer:
Answer:
The answer is
<h2>y + 2x = 2</h2>Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
The original line is 2x + y = 1
We must first write the equation in the general form above
That's
y = - 2x + 1
Comparing with the general equation above
Slope = - 2
Since the lines are parallel their slope are also the same
Slope of parallel line = - 2
So the equation of the line using point
( - 1 , 4) and slope - 2 is
<h3>We have the final answer as
<h3>y + 2x = 2</h3>Hope this helps you
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Answer:
(18, 14)
Step-by-step explanation:
We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.
The distance formula states that the distance between two points and
, the distance is denoted by:
. Let's find the distance between A and B:
d =
Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:
4√13 =
Square both sides:
208 = (6 - a)² + (6 - b)²
Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:
208 = (6 - a)² + (6 - b)²
208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²
208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52
0 = 13/9a² - 52/3a - 156
13a² - 156a - 1404 = 0
a² - 12a - 108 = 0
(a + 6)(a - 18) = 0
a = -6 or a = 18
We know a can't be negative so a = 18. Plug this back in to find b:
b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14
So point D has coordinates (18, 14).