i have a question in math

(( distance between two points ))

A quardilateral has vertices P(3,5), Q(-4,3), R(-3,-2), and S(5,-4). find the lengths of the diagonals,to the nearest tenth .

please in detales .. thank u

User Icon for Reiny Reiny answered
16 years ago

PR = √((5+2)^2 + (3+3)^2)

= √85

You do SQ and let me know what you got

User Icon for mota mota answered
16 years ago

it is easy thank u

i will do it
:)

QS = �ã((-4+5)^2 + (3+4)^2)
=�ã50

User Icon for mota mota answered
16 years ago

hi

i think theere is something wrong in the answer

PR = �ã((5+2)^2 + (3+3)^2)
= �ã85

because the rule is
�ã((x2-x1)^2 + (y2-y1)^2)

User Icon for Anonymous Anonymous answered
8 years ago

3892

User Icon for Explain Bot Explain Bot answered
11 months ago

To find the lengths of the diagonals of the given quadrilateral, we need to find the distance between each pair of vertices.

Let's start with the diagonal connecting points P and R. The distance formula is used to find the distance between two points in a Cartesian coordinate system. The formula is:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For the diagonal PR, we have the coordinates P(3,5) and R(-3,-2). Substituting these values into the distance formula, we get:

distance PR = sqrt((-3 - 3)^2 + (-2 - 5)^2)
= sqrt((-6)^2 + (-7)^2)
= sqrt(36 + 49)
= sqrt(85)
≈ 9.2 (rounded to the nearest tenth)

Now let's find the length of the other diagonal, QS. We have the coordinates Q(-4,3) and S(5,-4). Substituting these values into the distance formula, we get:

distance QS = sqrt((5 - (-4))^2 + (-4 - 3)^2)
= sqrt((5 + 4)^2 + (-4 - 3)^2)
= sqrt((9)^2 + (-7)^2)
= sqrt(81 + 49)
= sqrt(130)
≈ 11.4 (rounded to the nearest tenth)

Therefore, the lengths of the diagonals PR and QS are approximately 9.2 and 11.4 units, respectively.