A line passes through the points (-4,-1) and (4,3). A second line passes through the points (-2,-2) and (2,6). At what point do the two lines intersect

(-2/3 , 2/3)

Step-by-step explanation:

Line 1: (-4,-1) (4,3)

m = (3 - -1) / (4 - -4) = 4/8 = 1/2

equation: (y-3)/(x-4) = 1/2          y-3 = 1/2 x - 2

y = 1/2 x + 1 (1)

Line 2: (-2,-2) (2,6)

m = (6 - -2) / (2 - -2) = 8/4 = 2

equation: (y-6)/(x-2) = 2              y-6 = 2x - 4

y = 2x + 2  ...(2)

(2)-(1): 0 = 3/2x + 1

3/2 x = -1            x = - 2/3

y = 1/2 * (-2/3) + 1 = 2/3

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°