What is the perimeter of triangle PQR with vertices P(–2, 9), Q(7, –3), and R(–2, –3) in the coordinate plane? (1 point)
21 units
25 units
34 units
36 units
Zachary has graph the apartment building 2 units to the left and 5 units down from the grocery store.he has graphed the grocery store at (7,8).give the ordered pair for the apartment building.
To find the perimeter of a triangle, we need to calculate the lengths of all three sides and then add them up.
Using the distance formula, we can find the lengths of the triangle's sides:
Side PQ: [$\sqrt{(7-(-2))^2+(-3-9)^2}$]
= $\sqrt{9^2+(-12)^2}$
= $\sqrt{81+144}$
= $\sqrt{225}$
= 15 units
Side QR: [$\sqrt{((-2)-7)^2+((-3)-(-3))^2}$]
= $\sqrt{(-9)^2+(0)^2}$
= $\sqrt{81+0}$
= $\sqrt{81}$
= 9 units
Side RP: [$\sqrt{((-2)-(-2))^2+((-3)-9)^2}$]
= $\sqrt{0^2+(-12)^2}$
= $\sqrt{0+144}$
= $\sqrt{144}$
= 12 units
Now, we can add the lengths of the three sides to find the perimeter:
PQ + QR + RP = 15 + 9 + 12 = 36 units
Therefore, the perimeter of triangle PQR is 36 units.
To find the perimeter of a triangle, we need to add up the lengths of all three sides. To do this, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the lengths of each side of triangle PQR:
Side PQ:
- P(–2, 9)
- Q(7, –3)
Using the distance formula:
dPQ = √((7 - -2)^2 + (-3 - 9)^2)
= √(9^2 + (-12)^2)
= √(81 + 144)
= √225
= 15
Side QR:
- Q(7, –3)
- R(–2, –3)
Using the distance formula:
dQR = √((-2 - 7)^2 + (-3 - -3)^2)
= √((-9)^2 + 0^2)
= √(81 + 0)
= √81
= 9
Side RP:
- R(–2, –3)
- P(–2, 9)
Using the distance formula:
dRP = √((–2 - –2)^2 + (9 - –3)^2)
= √(0^2 + 12^2)
= √(0 + 144)
= √144
= 12
Now, let's add up the lengths of all three sides:
Perimeter = PQ + QR + RP
= 15 + 9 + 12
= 36 units
Therefore, the perimeter of triangle PQR is 36 units.