Z is centroid of triangle RST. What is RW, if RV=4x+3, WS=5x-1, and VT=2x+9?
1 answer:
Part (a):
We are given that Z is the <span>centroid of triangle RST. This means that Z is the point of intersection of the three medians of the triangle.
In other words:
W is the midpoint of RS
V is the midpoint of RT
We are given that:
RV = 4x + 3 and VT = 2x + 9
Since V is the midpoint, then:
RV = VT
4x + 3 = 2x + 9
4x - 2x = 9 - 3
2x = 6
x = 3
Part (b):
We are given that:
WS = 5x-1
x = 3
Therefore:
WS = 5(3) - 1
WS = 15 - 1 = 14
Part (c):
Since W is the midpoint of RS, therefore RW = WS
We calculated WS = 14
Therefore:
RW = 14
</span>
We are given that Z is the <span>centroid of triangle RST. This means that Z is the point of intersection of the three medians of the triangle.
In other words:
W is the midpoint of RS
V is the midpoint of RT
We are given that:
RV = 4x + 3 and VT = 2x + 9
Since V is the midpoint, then:
RV = VT
4x + 3 = 2x + 9
4x - 2x = 9 - 3
2x = 6
x = 3
Part (b):
We are given that:
WS = 5x-1
x = 3
Therefore:
WS = 5(3) - 1
WS = 15 - 1 = 14
Part (c):
Since W is the midpoint of RS, therefore RW = WS
We calculated WS = 14
Therefore:
RW = 14
</span>
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Answer:
<em>The required points of the given line segment are ( - 1, - 5 ).</em>
Step-by-step explanation:
Given that the line segment AB whose midpoint M is ( 3, -2 ) and point A is ( 7, - 9), then we have to find point B of the line segment AB -
As we know that-
If a line segment AB is with endpoints ( ) and (
)then the mid points M are-
<em>M = ( ,
)</em>
Here,
<em>Let A ( 7, - 9 ), B ( x, y ) with midpoint M ( 3, - 2 ) -</em>
then by the midpoint formula M are-
<em>( 3, - 2 ) = ( ,
)</em>
On comparing x coordinate and y coordinate -
We get,
<em>( = 3 ,
= - 2)</em>
<em>( 7 + x = 6, - 9 + y = - 4 )</em>
<em>( x = 6 - 7, y = - 4 + 9 )</em>
<em>( x = - 1, y = -5 )</em>
<em>Hence the required points A are ( - 1, - 5 ).</em>
<em>We can also verify by putting these points into Midpoint formula.</em>
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