the diagram shows triangle ABC point c has coordinates (4,7) and the equation of the line AB is x+2y=8 find the coordinates of B
I believe the way to solve x + 2y = 8 is,
2y = -x + 8
2y/2 = (-x + 8)/2
y = -x/2 + 4 => y = (-1/2)x + 4
Set the equation to zero:
(-1/2)x + 4 = 0
(-1/2)x = -4
Divide both sides by -1/2 to obtain the x value:
x = 8
Therefore, B(8,0) is your coordinate.
No idea. All I have is a point and a line. A and B could be anywhere on the line.
To find the coordinates of point B, we need to find the intersection point of line AB with the line passing through point C.
Given that the equation of line AB is x + 2y = 8, we can rearrange this equation into slope-intercept form (y = mx + b) by solving for y:
x + 2y = 8
2y = -x + 8
y = -(1/2)x + 4
Now, let's find the slope and y-intercept of line AB. Comparing the equation to the slope-intercept form, we can see that the slope of line AB is -1/2 and the y-intercept is 4.
The line passing through point C (4, 7) will have the same slope as line AB since they are parallel.
Now, we can use the point-slope formula (y - y₁ = m(x - x₁)) to find the equation of the line passing through point C:
(y - 7) = (-1/2)(x - 4)
or, simplifying:
2y - 14 = -x + 4
Rearranging this equation, we get:
2y + x = 18
Now, we need to find the intersection point of line AB and line passing through point C. To do this, we can solve the system of equations:
y = -(1/2)x + 4
2y + x = 18
Substituting the first equation into the second equation, we have:
2(-(1/2)x + 4) + x = 18
Simplifying, we get:
- (x - 8) + x = 18
- x + 8 + x = 18
2x = 18 - 8
2x = 10
x = 5
Now, we can substitute the value of x into the first equation to find y:
y = -(1/2)(5) + 4
y = -5/2 + 4
y = -5/2 + 8/2
y = 3/2
Therefore, the coordinates of point B are (5, 3/2).
To find the coordinates of point B, we need to determine the point of intersection between the line AB and the line BC. First, let's rearrange the equation of the line AB, x + 2y = 8, to the slope-intercept form, y = mx + b.
To do this, isolate the y variable:
2y = -x + 8
y = (-1/2)x + 4
Now, we can compare the equation of the line BC and the equation of the line AB to find the point of intersection. The equation of line BC is not given in the problem, so we will need additional information to find it.
Please provide the equation of line BC or any other relevant information necessary to determine the coordinates of point B.