Explore IDNLearn.com's extensive Q&A database and find the answers you need. Discover detailed answers to your questions with our extensive database of expert knowledge.
Sagot :
To determine the distance between two points in the coordinate plane, Martin can use the distance formula. The distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
In this problem, point [tex]\(D\)[/tex] has coordinates [tex]\((0, b)\)[/tex] and point [tex]\(A\)[/tex] has coordinates [tex]\((0, 0)\)[/tex].
Let's apply the distance formula step-by-step:
1. Identify the coordinates of points [tex]\(D\)[/tex] and [tex]\(A\)[/tex]:
- Coordinates of [tex]\(D\)[/tex]: [tex]\( (0, b) \)[/tex]
- Coordinates of [tex]\(A\)[/tex]: [tex]\( (0, 0) \)[/tex]
2. Substitute the coordinates into the distance formula:
- [tex]\( x_1 = 0 \)[/tex]
- [tex]\( y_1 = b \)[/tex]
- [tex]\( x_2 = 0 \)[/tex]
- [tex]\( y_2 = 0 \)[/tex]
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
3. Substitute the specific coordinates into the formula:
[tex]\[ \text{Distance} = \sqrt{(0 - 0)^2 + (b - 0)^2} \][/tex]
4. Simplify the expression inside the square root:
[tex]\[ \text{Distance} = \sqrt{0 + b^2} \][/tex]
5. Simplify further:
[tex]\[ \text{Distance} = \sqrt{b^2} \][/tex]
6. Since the square root of [tex]\(b^2\)[/tex] is [tex]\(b\)[/tex] (assuming [tex]\(b \geq 0\)[/tex]):
[tex]\[ \text{Distance} = b \][/tex]
Therefore, the correct formula Martin can use to determine the distance from point [tex]\(D\)[/tex] to point [tex]\(A\)[/tex] is:
[tex]\[ \sqrt{(0-0)^2+(b-0)^2}=\sqrt{b^2}=b \][/tex]
Hence, the correct answer is:
A. [tex]\(\sqrt{(0-0)^2+(b-0)^2}=\sqrt{b^2}=b\)[/tex]
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
In this problem, point [tex]\(D\)[/tex] has coordinates [tex]\((0, b)\)[/tex] and point [tex]\(A\)[/tex] has coordinates [tex]\((0, 0)\)[/tex].
Let's apply the distance formula step-by-step:
1. Identify the coordinates of points [tex]\(D\)[/tex] and [tex]\(A\)[/tex]:
- Coordinates of [tex]\(D\)[/tex]: [tex]\( (0, b) \)[/tex]
- Coordinates of [tex]\(A\)[/tex]: [tex]\( (0, 0) \)[/tex]
2. Substitute the coordinates into the distance formula:
- [tex]\( x_1 = 0 \)[/tex]
- [tex]\( y_1 = b \)[/tex]
- [tex]\( x_2 = 0 \)[/tex]
- [tex]\( y_2 = 0 \)[/tex]
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
3. Substitute the specific coordinates into the formula:
[tex]\[ \text{Distance} = \sqrt{(0 - 0)^2 + (b - 0)^2} \][/tex]
4. Simplify the expression inside the square root:
[tex]\[ \text{Distance} = \sqrt{0 + b^2} \][/tex]
5. Simplify further:
[tex]\[ \text{Distance} = \sqrt{b^2} \][/tex]
6. Since the square root of [tex]\(b^2\)[/tex] is [tex]\(b\)[/tex] (assuming [tex]\(b \geq 0\)[/tex]):
[tex]\[ \text{Distance} = b \][/tex]
Therefore, the correct formula Martin can use to determine the distance from point [tex]\(D\)[/tex] to point [tex]\(A\)[/tex] is:
[tex]\[ \sqrt{(0-0)^2+(b-0)^2}=\sqrt{b^2}=b \][/tex]
Hence, the correct answer is:
A. [tex]\(\sqrt{(0-0)^2+(b-0)^2}=\sqrt{b^2}=b\)[/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.