Find the cardinal number of the given set. A = {{3, 5, 7, ... 25}}
1 answer:
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Given parameters:
Midpoint of AB = M(3, -1)
Coordinates of A = (5,1)
Unknown:
Coordinates of B = ?
Solution:
To find the mid point of any line, we use the expression below;
and
where and
= coordinates of the mid points = 3 and -1
x₁ = 5 and y₁ = 1
x₂ = ? and y₂ = ?
Now let us input the variables and solve,
3 = and -1 =
5 + x₂ = 6 -2 = 1 + y₂
x₂ = 1 y₂ = -2 -1 = -3
The coordinates of B = 1, -3
If the triangles are similar, the proportion of the legs on the left to the legs on the right will be equal. This proportion would look like:
(You needed to combine the orange segment and the yellow segment to find the total length of the large triangle).
Now, cross multiply and solve for x:
28x+14=30x
<em>*Subtract 28x from both sides to isolate the variable*</em>
14=2x
<em>*Divide both sides by 2*</em>
7=x
Hope this helps!!