Which points lie on the line that passes through point p and
is parallel to the given line? select three options.
(-4,2)
(-1,3)
(-2, 2)
(4,2)
(-5, -1)

Option 2nd , 3rd and 5th are correct.

Step-by-step explanation:

Given:

Given line passes through points ( -2 , -4 ) and ( 4 , 2 )

Coordinate of the Point P( 0 , 4 )

To find: Point which lie on the line parallel to given line and passes through point P.

Slope of the given line =

We know that slope of parallel lines ara equal.

So, Using Slope-Point form we get equation of line,

y - 4 = 1 ( x - 0 )

y - 4 = x

x - y = -4

Option 1:

x = -4 , y = 2

LHS = -4 - 2 = -6 ≠ RHS

Thus, This is not required point.

Option 2:

x = -1 , y = 3

LHS = -1 - 3 = -4 = RHS

Thus, This is required point.

Option 3:

x = -2 , y = 2

LHS = -2 - 2 = -4 = RHS

Thus, This is required point.

Option 4:

x = 4 , y = 2

LHS = 4 - 2 = 2 ≠ RHS

Thus, This is not required point.

Option 5:

x = -5 , y = -1

LHS = -5 - (-1) = -4 = RHS

Thus, This is required point.

Therefore, Option 2nd , 3rd and 5th are correct.

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°

answer: rolling a number cube and flipping a coin.

step-by-step explanation: