Triangle N Q L has centroid S. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments N R, L P, and Q M. The length of line segment N S is 9 n minus 12 and the length of line segment S R is 3 n.
S is the centroid of triangle NQL.
What is the length of NR?
4 units
8 units
36 units
48 units

yes

step-by-step explanation:

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²

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