DaQuan marks two points on the coordinate plane. One point is L(4,2) and the other point is M(7,6) . What is the correct way for DaQuan to set up the distance formula?(1 point) Responses d=(4−7)2+(2−6)2−−−−−−−−−−−−−−−√ d is equal to square root of open paren 4 minus 7 close paren squared plus open paren 2 minus 6 close paren squared end root d=(2−4)2+(6−7)2−−−−−−−−−−−−−−−√ d is equal to square root of open paren 2 minus 4 close paren squared plus open paren 6 minus 7 close paren squared end root d=(6−7)2+(2−4)2−−−−−−−−−−−−−−−√ d is equal to square root of open paren 6 minus 7 close paren squared plus open paren 2 minus 4 close paren squared end root d=(2−7)2+(4−6)2−−−−−−−−−−−−−−−√

Question

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Answer 1

The distance formula between two points \(L(x_1, y_1)\) and \(M(x_2, y_2)\) on the coordinate plane is given by the formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

In this case, we have the points \(L(4, 2)\) and \(M(7, 6)\). So we can identify:

• \(x_1 = 4\)
• \(y_1 = 2\)
• \(x_2 = 7\)
• \(y_2 = 6\)

Substituting these values into the distance formula gives:

\[ d = \sqrt{(7 - 4)^2 + (6 - 2)^2} \]

Which simplifies to:

\[ d = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

Looking at the options:

1. \(d = \sqrt{(4−7)^2 + (2−6)^2}\)
2. \(d = \sqrt{(2−4)^2 + (6−7)^2}\)
3. \(d = \sqrt{(6−7)^2 + (2−4)^2}\)
4. \(d = \sqrt{(2−7)^2 + (4−6)^2}\)

The correct setup of the distance formula considering points \(L(4, 2)\) and \(M(7, 6)\) is:

Response 1: \(d = \sqrt{(4 - 7)^2 + (2 - 6)^2}\)