ABCD is a rectangle. A is the point (0,1). c is the point (0,6) the equation of the straight line through A and B is y=2x+1.
(a)Find the equation of the straight line through D and C
Why did the line go to therapy?
Because it had trouble with its slope! *ba dum tss*
To find the equation of the straight line through D and C, we need to determine the slope and one point on the line. Let's start with the slope!
The slope of the line passing through points A and B is equal to the coefficient of x in its equation, which is 2. Since ABCD is a rectangle, the opposite sides are parallel, so the slope of the line through D and C will be the same - 2.
Now, let's find a point on the line. Point D has the same y-coordinate as A, which is 1. So the coordinates of point D are (x, 1).
Using the slope-intercept form of a straight line equation, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the slope and the coordinates of point D to find the equation of the line:
1 = 2x + b
To find the value of b, let's use the information given. Point C has coordinates (0, 6). Substituting these coordinates into the equation, we get:
6 = 2(0) + b
6 = b
So, the equation of the straight line passing through points D and C is:
y = 2x + 6
To find the equation of the straight line through D and C, we need to find the slope of the line and a point on the line.
Given that ABCD is a rectangle, we know that AB is parallel to CD. Since the equation of the line through A and B is y = 2x + 1, the slope of AB is 2.
Since AB is parallel to CD, the slope of CD is also 2.
Next, we need to find a point on the line. We know that C is the point (0, 6). Since C is on the line CD, we can use this point as our reference.
Therefore, the equation of the straight line through D and C is y = 2x + 6.
To find the equation of the straight line through D and C, we need to determine the slope and y-intercept of the line.
First, let's find the coordinates of point B in the rectangle ABCD. As A is given as (0,1), and ABCD is a rectangle, B will have the same x-coordinate as A but with the y-coordinate being equal to the y-coordinate of C, which is 6. Thus, the coordinates of point B are (0,6).
Next, we can find the slope of the line passing through A and B using the slope formula:
m = (y2 - y1) / (x2 - x1)
= (6 - 1) / (0 - 0)
= 5 / 0
As the denominator is zero, the slope is undefined.
Since the slope is undefined, this means the line is vertical and parallel to the y-axis. Therefore, the equation of the line passing through D and C can be written as x = k, where k is the x-coordinate of D (since the line is vertical and all x-coordinates will have the same value).
To find the value of k, we can look at the coordinates of point D. As D lies on the same line as C, the x-coordinate of D will also be 0. Thus, the equation of the straight line passing through D and C is x = 0.
CD//AB
m1 = 2 = Slope of AB.
m2 = -1/2 = slope of CD.
Y = (-1/2)0 + b = 6,
b = 6.
Eq: Y = (-1/2)X + 6.