Answer:
(6, 2.5 )
Step-by-step explanation:
Given y varies inversely as x then the equation relating them is
y = ← k is the constant of variation
To find k substitute the coordinate point (5, 3 ) into the equation, that is
3 = ( multiply both sides by 5 )
15 = k
y = ← equation of variation
Using (x, 2.5 ) with y = 2.5 , then
2.5 = ( multiply both sides by x )
2.5x = 15 ( divide both sides by 2.5 )
x = 6
Thus point is (6, 2.5 )
Answer:
Proved
Step-by-step explanation:
Given: EC || AC, DB || AC, ∠A = ∠F
Prove: ΔMDF ∼ ΔNCA
Solution
See diagram attached to the solution to better understand the following workings.
Redrawing ΔMDF or rotating to be facing the same direction.
EC is parallel to AC
DB parallel to AC
Using similar triangle theorem:
If ΔMDF ∼ ΔNCA
Ratio of Corresponding sides would be equal
(adjacent of ΔMDF)/(adjacent of ΔNCA) = (Opposite of ΔMDF)/(opposite of ΔNCA) = (hypotenuse of ΔMDF)/(hypotenuse of ΔNCA)
DF/ CA = MD/NC = FM/AN
∠A = ∠F
∠M = ∠N
∠D = ∠C
Since the ratio of Corresponding sides and angle are equal, ΔMDF is similar to ΔNCA.
ΔMDF ∼ ΔNCA
