Question

please answer me 4,5 both please guys??

Answer 1

Answer:

4. (3,5)

5. 3/5

Step-by-step explanation:

(4)

Given vertices are A(1,2),B(4,3) and C(6,6).

Let (x,y) be the coordinates of vertex D.

∴ Mid-point of AC = (1 + 6/2, 2 + 6/2)

                              = (7/2,4).

∴ Mid-point of BD = (x + 4/2, y + 3/2)

We know that In a parallelogram diagonals bisect each other.

∴ Midpoint of BD = Midpoint of AC.

⇒ (x + 4/2, y + 3/2) = (7/2,4)

(i)

(x + 4)/2 = 7/2

⇒ 2x + 8 = 14

⇒ 2x = 6

⇒ x = 3.

(ii)

⇒ (y + 3)/2 = 4

⇒ y + 3 = 8

⇒ y = 5.

Therefore, the fourth vertex is D(3,5).

(5)

Given, cot θ = 1/√3

⇒ cot θ = cot 60°

⇒ θ = 60°.

Now,

Given : (1 - cos² θ)/(2 - sin² θ)

= [1 - (1/2)²]/[2 - (√3/2)²]

= [1 - 1/4]/[2 - 3/4]

= [3/4]/[5/4]

= 3/5

Hope it helps!

Answer 2

Step-by-step explanation:

BD midpoint 4+3/2=7/2

AC midpoint 1+x/2=7/2

=7=1+x

x=6units

AC y axis 6+2/2

y=4 units

BD y axis 5+y/2=4

5+y=8

y=3units