Question

Line ℓ has equation y= - x+3. find the distance between ℓ and the point r(5,3). round your answer to the nearest tenth.

Answer 1

The distance between line ℓ and point R(5,3) is 5 units.

Step-by-step explanation:

To find the distance between the line ℓ and the point R(5,3), we can use the formula for the distance between a point and a line in slope-intercept form. The equation of line ℓ is y = -x + 3. We can determine the y-coordinate of the point on line ℓ that is closest to point R by substituting the x-coordinate of point R into the equation of line ℓ. So, when x = 5, y = -5 + 3 = -2. Therefore, the coordinates of the closest point on line ℓ to point R are (5,-2).

Now, we can use the distance formula to calculate the distance between the two points. The distance formula is given by d = sqrt((x2-x1)^2 + (y2-y1)^2), where (x1,y1) and (x2,y2) are the coordinates of the two points. Using (5,3) as (x1,y1) and (5,-2) as (x2,y2), we have:

d = sqrt((5-5)^2 + (-2-3)^2) = sqrt(0 + 25) = sqrt(25) = 5.

Therefore, the distance between line ℓ and point R(5,3) is 5 units.

Answer 2

`y + x - 3 = 0`
the the distance will be

`5 / √(2)`