Shortest distance between Y=-1/2x-3 and the point R(4,5) Calculate the shortest distance between each point and the given line? Please help step by step with graph.
To calculate the distance from the point R(4,5) to the line `y=-1/2x-3` , we need to find the perpendicular line that intersects R and the line `y=-1/2x-3` . This intersection happens at a point, let's call it Q. The slope of `y=-1/2x-3` is `-1/2` , so the slope of RQ is 2. We can use this with R to find the equation of RQ.
So the equation of the line RQ is `y=2x-3` . Noticing that both the original line `y=-1/2x-3` and `y=2x-3` have the same y-intercept (0,-3). This means that Q is (0,-3), which is the intersection point of the two lines.
The shortest distance from R to the line is the distance from R to Q, which we find using the distance formula:
The distance from R to the line is `4sqrt5` . The graph is: