Find answers to your most challenging questions with the help of IDNLearn.com's experts. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.
Sagot :
To find the length of the line segment [tex]\(\overline{WX}\)[/tex] with endpoints [tex]\(W(5, -3)\)[/tex] and [tex]\(X(-1, -9)\)[/tex], we follow these steps:
1. Identify the coordinates of points [tex]\(W\)[/tex] and [tex]\(X\)[/tex]:
- [tex]\(W = (5, -3)\)[/tex]
- [tex]\(X = (-1, -9)\)[/tex]
2. Calculate the differences in the x-coordinates and y-coordinates:
- [tex]\(\Delta x = X_x - W_x = -1 - 5 = -6\)[/tex]
- [tex]\(\Delta y = X_y - W_y = -9 - (-3) = -9 + 3 = -6\)[/tex]
3. Recall the distance formula for the length of a line segment between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
4. Substitute the values [tex]\(\Delta x\)[/tex] and [tex]\(\Delta y\)[/tex] into the distance formula:
[tex]\[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(-6)^2 + (-6)^2} \][/tex]
5. Simplify the expression:
[tex]\[ d = \sqrt{36 + 36} = \sqrt{72} \][/tex]
6. Simplify [tex]\(\sqrt{72}\)[/tex]:
[tex]\[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2} \][/tex]
7. Approximate the square root of 2 to obtain a numerical value:
[tex]\[ \sqrt{2} \approx 1.414 \][/tex]
Thus,
[tex]\[ 6 \times 1.414 \approx 8.485 \][/tex]
So, the calculated length of [tex]\(\overline{WX}\)[/tex] is approximately [tex]\(8.485\)[/tex].
Therefore, the length of [tex]\(\overline{WX}\)[/tex] is [tex]\(\boxed{8.485}\)[/tex], not 6.
1. Identify the coordinates of points [tex]\(W\)[/tex] and [tex]\(X\)[/tex]:
- [tex]\(W = (5, -3)\)[/tex]
- [tex]\(X = (-1, -9)\)[/tex]
2. Calculate the differences in the x-coordinates and y-coordinates:
- [tex]\(\Delta x = X_x - W_x = -1 - 5 = -6\)[/tex]
- [tex]\(\Delta y = X_y - W_y = -9 - (-3) = -9 + 3 = -6\)[/tex]
3. Recall the distance formula for the length of a line segment between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
4. Substitute the values [tex]\(\Delta x\)[/tex] and [tex]\(\Delta y\)[/tex] into the distance formula:
[tex]\[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(-6)^2 + (-6)^2} \][/tex]
5. Simplify the expression:
[tex]\[ d = \sqrt{36 + 36} = \sqrt{72} \][/tex]
6. Simplify [tex]\(\sqrt{72}\)[/tex]:
[tex]\[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2} \][/tex]
7. Approximate the square root of 2 to obtain a numerical value:
[tex]\[ \sqrt{2} \approx 1.414 \][/tex]
Thus,
[tex]\[ 6 \times 1.414 \approx 8.485 \][/tex]
So, the calculated length of [tex]\(\overline{WX}\)[/tex] is approximately [tex]\(8.485\)[/tex].
Therefore, the length of [tex]\(\overline{WX}\)[/tex] is [tex]\(\boxed{8.485}\)[/tex], not 6.
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.