The works with of he vertices the triangle PQR are P (0,-5), Q(-2,3) and also R (3,-2). What is the perimeter of triangle PQR (IN most basic radical form if necessary)
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You are watching: What are the vertices of pqr You need to evaluate the perimeter of triangle PQR, hence, you require to discover the lengths the the sides of triangle, using distance formula, such that:

`PQ = sqrt((x_Q - x_P)^2 + (y_Q - y_P)^2)`

`PQ = sqrt(4 + 64) => PQ = sqrt 68 = 2sqrt17`

`PR = sqrt((x_R...

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You must evaluate the perimeter of triangle PQR, hence, you require to uncover the lengths the the sides of triangle, utilizing distance formula, together that:

`PQ = sqrt((x_Q - x_P)^2 + (y_Q - y_P)^2)`

`PQ = sqrt(4 + 64) => PQ = sqrt 68 = 2sqrt17`

`PR = sqrt((x_R - x_P)^2 + (y_R - y_P)^2)`

`PR = sqrt(9 + 9) => PR = sqrt18 = 3sqrt2`

`RQ = sqrt((x_Q - x_R)^2 + (y_Q - y_R)^2)`

`RQ = sqrt(25 + 25) => RQ = 5sqrt2`

Evaluating the perimeter the triangle PQR yields:

`P_(PQR) = PQ + QR + PR => P_(PQR) = 2sqrt17 + 5sqrt2 + 3sqrt2`

Combining the members that contain the exact same radical, yields:

`P_(PQR) = 2sqrt17 + 8sqrt2`

Factoring out 2 yields:

`P_(PQR) = 2(sqrt17 + 4sqrt2) => P_(PQR) = 2(sqrt17 + sqrt(4^2*2))`

`P_(PQR) = 2(sqrt17 + sqrt32)`

Hence, evaluating the perimeter the triangle PQR, utilizing distance formula, returns `P_(PQR) = 2(sqrt17 + sqrt32).`

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