Line ℓ has equation y=x-3. Find the distance between ℓ and the point E(-1,3). Round your answer to the nearest tenth

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Line  ℓ has equation  y=x-3. Find the distance between  ℓ and the point  E(-1,3). Round your answer to the nearest tenth

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Write Equation and Coordinates: Write down the equation of line ℓ and the coordinates of point E. Line ℓ: y = x - 3 Point E: (-1, 3)Determine Line Slope: Determine the slope of line ℓ. The slope of line ℓ is the coefficient of x in the equation y = x - 3, which is 1.Find Perpendicular Slope: Find the slope of the line perpendicular to line ℓ. The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Since the slope of line ℓ is 1, the slope of the perpendicular line is -1.Write Perpendicular Line Equation: Write the equation of the line perpendicular to line ℓ that passes through point E(-1, 3). Using the point-slope form of a line's equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we get: y - 3 = -1(x - (-1)) y - 3 = -1(x + 1)Simplify Perpendicular Line: Simplify the equation of the perpendicular line. y - 3 = -x - 1 y = -x + 2 This is the equation of the line perpendicular to line ℓ that passes through point E.Find Point of Intersection: Find the point of intersection between line ℓ and the perpendicular line. To find the intersection, set the equations of line ℓ and the perpendicular line equal to each other: x - 3 = -x + 2 2x = 5 x = 5/2 Now, substitute x back into the equation of line ℓ to find y: y = (5/2) - 3 y = 5/2 - 6/2 y = -1/2 The point of intersection is (5/2, -1/2).Calculate Distance: Calculate the distance between point E and the point of intersection. Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) is point E and (x2, y2) is the point of intersection. d = √((5/2 - (-1))² + (-1/2 - 3)²) d = √((5/2 + 1)² + (-1/2 - 3)²) d = √((5/2 + 2/2)² + (-1/2 - 6/2)²) d = √((7/2)² + (-7/2)²) d = √((49/4) + (49/4)) d = √(98/4) d = √(49/2) d = √(24.5) d ≈ 4.95 Round to the nearest tenth: d ≈ 4.9

Line $\ell$ has equation $y=x-3$ . Find the distance between $\ell$ and the point $E(-1,3)$ . $\newline$ Round your answer to the nearest tenth

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Line ℓ \ell ℓ has equation y=x−3 y=x-3 y=x−3. Find the distance between ℓ \ell ℓ and the point E(−1,3) E(-1,3) E(−1,3).\newlineRound your answer to the nearest tenth

Line $\ell$ has equation $y=x-3$ . Find the distance between $\ell$ and the point $E(-1,3)$ . $\newline$ Round your answer to the nearest tenth