Question

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=(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=(2−4)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=(2−7)2+(4−6)2−−−−−−−−−−−−−−−√
d is equal to square root of open paren 2 minus 7 close paren squared plus open paren 4 minus 6 close paren squared end root

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
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page 17 of 17

Answer 1

To set up the distance formula correctly, we use the coordinates of points L(4,2) and M(7,6). The distance formula is given by:

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

Here, \( (x_1, y_1) = (4, 2) \) and \( (x_2, y_2) = (7, 6) \).

Substituting the coordinates into the distance formula, we have:

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

This simplifies to:

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

Based on the options provided, the correct way for DaQuan to set up the distance formula is:

**d = √((7 - 4)² + (6 - 2)²)**

However, from the options listed:

- The choice **d=(4−7)²+(2−6)²** corresponds to the correct application of the distance formula but incorrectly flips the points:

**d = √((4 - 7)² + (2 - 6)²)**

This is mathematically equivalent to using \((7 - 4)\) and \((6 - 2)\), so the correct response from the given options is:

**d=(4−7)²+(2−6)²**

So the answer is the last option:

**d = √((4 - 7)² + (2 - 6)²)**.