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The coordinates of the point W are (9,-2) and the coordinates of point X are (-4,-2). What is the distance, in units, between the point W and point X ? Answer: units

The coordinates of the point W W are (9,−2) (9,-2) and the coordinates of point X X are (−4,−2) (-4,-2) . What is the distance, in units, between the point W W and point X X ?\newlineAnswer: □\square units

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Full solution

Q. The coordinates of the point W W are (9,−2) (9,-2) and the coordinates of point X X are (−4,−2) (-4,-2) . What is the distance, in units, between the point W W and point X X ?\newlineAnswer: □\square units
  1. Distance Formula: To find the distance between two points in a coordinate plane, we use the distance formula, which is derived from the Pythagorean theorem. The distance formula is:\newlineDistance=(x2−x1)2+(y2−y1)2 \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \newlinewhere (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two points.
  2. Identify Coordinates: Let's identify the coordinates of points W and X. Point W has coordinates (99, −2-2) and point X has coordinates (−4-4, −2-2). We can label these as follows:\newlinex1=9x_1 = 9, y1=−2y_1 = -2\newlinex2=−4x_2 = -4, y2=−2y_2 = -2
  3. Substitute into Formula: Now we will substitute these coordinates into the distance formula:\newlineDistance=((−4)−9)2+((−2)−(−2))2 \text{Distance} = \sqrt{((-4) - 9)^2 + ((-2) - (-2))^2}
  4. Perform Calculations: Perform the calculations inside the square root:\newlineDistance=(−4−9)2+(−2+2)2 \text{Distance} = \sqrt{(-4 - 9)^2 + (-2 + 2)^2} \newlineDistance=(−13)2+(0)2 \text{Distance} = \sqrt{(-13)^2 + (0)^2} \newlineDistance=169+0 \text{Distance} = \sqrt{169 + 0}
  5. Simplify and Find Distance: Simplify the expression under the square root and then take the square root:\newlineDistance=169 \text{Distance} = \sqrt{169} \newlineDistance=13 \text{Distance} = 13

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