Distance Formula

The equation of the line is: So, we can parametrize the line as: Now, we need to find the image of the point in this line. Let the image point be . The point will be the reflection of on the line. First, calculate the direction ratios of the line: The parametric equations of the line passing through and the point are: To find the coordinates of the image , solve the equations for when the distance between and is minimized. After performing the necessary calculations (which involve solving for and substituting back), the coordinates of the image can be found. Next, find the equation of the line joining and . This can be done by finding the direction ratios of the line joining and and writing the parametric equations of the line. Thus, the image of is , and the equation of the line joining and is .

The equation of the line is: So, the parametric equations for the line are: Now, let be the point on the line. We are given that the distance between and is 7 units. The distance formula between two points and is: Substitute the coordinates of and : Substitute the parametric equations of into this equation, and solve for . After simplifying the expression, you will get the value of , and then substitute back into the parametric equations to find the coordinates of . Finally, find the equation of the line joining and . This can be done using the parametric form of the line: Substitute the coordinates of and to get the equation of the line joining and .