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Could someone help me with this "Linear function problem"?
The equation of two adjacent sides of a rhombus are y=2x + 4 and y = -(x/3) +4 .
If A(12,0) is one vertex and all the vertices have positive co-ordinates, find the co-ordinates of the other 3 sides.
Plz, include full working out.
Thnx...
3 Answers
- Jerome JLv 71 decade agoFavorite Answer
y = 2x + 4
y = -x/3 + 4
2x + 4 = -x/3 + 4
6x + 12 = -x + 12
7x = 0
x = 0
y = 2(0) + 4
y = 4
Therefore other vertex = (0, 4)
Distance from, (0, 4) to (12, 0) = √(4² + 12²) = √160 = 4√10
3rd vertex on y = 2x + 4
(h - 0)² + (k - 4)² = 160
h² + k² = 160
h² + (2h + 4 - 4)² = 160
h² + 4h² = 160
5h² = 160
h² = 32
h = 4√2
k = 2(4√2) + 4 = 8√2 + 4
Therefore third vertex = (h, k) = (4√2, 8√2 + 4)
Fourth vertex = (12 + (4√2 - 0), 0 + (8√2 + 4- 4))
= (12 + (4√2, 8√2)
So all the vertexes are
A(12, 0),
(0, 4),
(4√2, 8√2 + 4),
(12 + (4√2, 8√2)
- vectLv 71 decade ago
the 2 lines intersect at (0,4)
find the distance between the 2 points(0,4),(12,0)
and it is sqrt160
draw out the graph.The other 2 points are on the right side of the graph
slope of one of the side is y=2x+b
use (12,0) as one of the point , find the line is y=2x-24
Use (a,b) as another vertex on this line
b=2a-24
160=(12-a)^2+b^2
solve and get (12+2sqrt3,4sqrt3)
and the other point is (2sqrt3,4+4sqrt3)
- DukeZhangLv 41 decade ago
hi, i'm little confused with "find the co-ordinates of the other 3 sides", are you asking the equation of the sides? or the vertices?