Question

Find the distance from point A(-9, -3) to the line y = x-6. Round your answer to the nearest tenth.

Answer 1

• 8.5 units

===========================

Given

• Point A(- 9, - 3) and
• Line y = x - 6

To find

• The distance between the given point and line.

Use the point - line distance formula

• 
  `d = \cfrac{√(a^2+b^2) }`

Where, x₁ and y₁ are the coordinates of the point, a, b, c are the coefficients of the line ax + by + c = 0

As per given the line is:

• y = x - 6 ⇒ x - y - 6 = 0, converted from slope-intercept to standard form, so

• a = 1, b = - 1, c = - 6 and

• x₁ = - 9, y₁ = - 3

Plug in the values and calculate the distance:

• 
  `d = \cfrac{√(1^2+(-1)^2) }=`
• 
  `\cfrac{√(1+1) }=`
• 
  `\cfrac-12{√(2) }=`
• 
  `\cfrac{12}{√(2) }=`
• 8.5 (rounded)