Question

PLEASE HELP

Use the distance formula to
find the length of line segment
JP. If your answer turns out to
be a square root that does not
equal a whole number, estimate
it to one decimal place.
J(-2,4) TY
D(4,4)
P(3,-2)
X

Answer 1

To find the length of line segment JP, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, we have:
J(-2, 4) and P(3, -2)
So:
d = sqrt((3 - (-2))^2 + (-2 - 4)^2)
= sqrt(5^2 + (-6)^2)
= sqrt(25 + 36)
= sqrt(61)
≈ 7.8
Therefore, the length of line segment JP is approximately 7.8 units.

Answer 2

`\begin{aligned}d(J, P) &= √(61) \\ &\approx 7.8 \end{aligned}`

Explanation:

The distance formula is:

`d(A, B) = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

where
`A = (x_1, y_1)` and
`B = (x_2, y_2)`.

From the given graph, we can identify the following coordinates for
`A` and
`B`:

`A = J = (-2, 4)`

`B = P = (3, -2)`

From these coordinates, we can assign the following variables values:

`x_1 = -2`,
`y_1 = 4`

`x_2 = 3`,
`y_2 = -2`

Plugging these values into the distance formula:

`d(J, P) = √((3 - (-2))^2 + (-2 - 4)^2)`

`d(J, P) = √((3 + 2)^2 + (-6)^2)`

`d(J, P) = √(5^2 + (-6)^2)`

`d(J, P) = √(25 + 36)`

`\boxed{ \begin{aligned}d(J, P) &= √(61) \\ &\approx 7.8 \end{aligned}}`