A(1, 1)
b (1, 3)
c (4, 3)
rectangle abcd has the coordinates shown.

find the coordinates of point d.
a) (5, 1)
b) (4, 2)
c) (3, 1)
d) (4, 1)

The coordinate of D is (4,1)

D is correct

Step-by-step explanation:

A (1, 1)  

B (1, 3)  

C (4, 3)

ABCD is a rectangle.

Let coordinate of D be (x,y)

As we know mid point of both diagonal is same.

In rectangle ABCD

Diagonals are AC and BD.

So, Mid point of AC =  Mid point of BD

Formula:

Hence, The coordinate of D is (4,1)

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°