Coordinate Geometry: Find A & B on 5x-12y=6 & 3x-4y=-2

In summary, the points A and B are located on the line 5x-12y=6 and have perpendicular distances of 4 units from the line 3x-4y=-2. A and B also lie on opposite sides of the second line, with A on the same side as the origin and B on the other side. The coordinates of A and B are not provided.
  • #1
thereddevils
438
0

Homework Statement



The points A and B are located on the line 5x-12y=6.The perpendicular distances of A and B respectively from the line 3x-4y=-2 are both 4 units. A lies on the same side of 3x-4y=-2 as the origin ,and B lies on the other side. Find the coordinates of A and B.

Homework Equations





The Attempt at a Solution



I do not understand what it means by the line in red. It has been previously stated both A and B lies on the same line so now how can they be on different sides relative to the origin?
 
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  • #2
A and B lie on the first line, but on each side of the second line.
 

Related to Coordinate Geometry: Find A & B on 5x-12y=6 & 3x-4y=-2

1. How do you find the coordinates of point A and B on the line 5x-12y=6?

In order to find the coordinates of point A and B, we need to first solve for x and y in the equation. To do this, we can rearrange the equation into the slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept. Once we have the equations in this form, we can set y=0 to find the x-intercept, which will give us the x-coordinate for point A. Then, we can set x=0 to find the y-intercept, which will give us the y-coordinate for point B.

2. What is the slope of the line 5x-12y=6?

The slope of a line is represented by the coefficient of x in the slope-intercept form, y=mx+b. In this case, the slope is equal to 5/12.

3. How can you graph the line 5x-12y=6?

To graph a line, we need at least two points on the line. We can use the coordinates of point A and B that we found in the first question to plot these points on a coordinate plane. Then, we can connect these points with a straight line to graph the line 5x-12y=6.

4. How do you find the point of intersection between the lines 5x-12y=6 and 3x-4y=-2?

To find the point of intersection between two lines, we can set the equations equal to each other and solve for x and y. This will give us the coordinates of the point where the lines intersect. In this case, the point of intersection is (2, -1).

5. Is it possible for the lines 5x-12y=6 and 3x-4y=-2 to be parallel?

In order for two lines to be parallel, they must have the same slope. However, for the lines 5x-12y=6 and 3x-4y=-2, the slopes are not equal. Therefore, these lines are not parallel.

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