If Z is the centroid of ∆LMN,WZ=4,ZN=14, and ZY = 10, find each missing measure
1 answer:
Answer:
ZM = 8
WM = 12
XZ = 7
XN = 21
LZ = 20
Step-by-step explanation:
The centroid of a triangle is the point of intersection of the midpoint of the each of the three sides of a triangle. The centroid of a triangle is located inside the triangle and it is known as the center of gravity.
The centroid theorem for a triangle states that the centroid of a triangle is located at 2/3 of the distance from the vertex of the triangle of the middle of the opposite side.
ZM = (2/3)WM (centroid theorem)
Therefore: WZ = (1/3)WM
WM = 3WZ = 3 * 4 = 12
ZM = (2/3) * WM = 2/3 * 12 = 8
ZN = (2/3)XN (centroid theorem)
XN = (3/2)ZN = 3/2 * 14 = 21
XN = 21
XZ + ZN = XN
XZ + 14 = 21
XZ = 7
LZ = (2/3)LY (centroid theorem)
Therefore: ZY = (1/3)LY
LY = 3ZY = 3 * 10 = 30
LZ = (2/3) * LY = 2/3 * 30 = 20
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Answer:
Step-by-step explanation:
f(x) = 4-x
g(x) = h+k
g(f(x)) = 2-16x+26
so put f(x) in g(x)
h+k
h((4-x)(4-x) + k
h(-8x+16)+k
if h = 2 , then
2-16x+32 + k
and we want 26 instead of 32 so subtract 6 so K = (-6)
2-16x+32 + (-6)
2-16x+32 - 6
2-16x+26
h=2
k=(-6)