Using the distance formula, the distance between (-3, 4) and (2, -3) is: 8.6 units.
<h3>What is the distance formula?</h3>Distance formula for calculating the distance between two points on a coordinate plane is given as: .
Let,
(-3, 4) = (x1, y1)
(2, -3) = (x2, y2)
Plug in the values
c = 8.6 units.
Therefore, using the distance formula, the distance between (-3, 4) and (2, -3) is: 8.6 units.
Learn more about distance formula on:
Answer:
" Vertical angles are congruent " ⇒ 2nd answer
Step-by-step explanation:
* <em>Look to the attached figure </em>
- There are three lines intersected at point D
- We need to find the missing in step 3
∵ Line FA intersects line EC at point D
- The angles formed when two lines cross each other are called
vertical angles
- Vertical angles are congruent (vertical angles theorem)
∴ ∠ADC and ∠FDE are vertical angles
∵ Vertical angles are congruent
∴ ∠EDF ≅ ∠ADC
∴ m∠EDF ≅ m∠ADC
∵ m∠EDF = 120° ⇒ given
∵ m∠ADC = m∠ADB + m∠BDC
∴ m∠ADB + m∠BDC = 120°
∵ m∠ADB = (3x)° ⇒ given
∵ m∠BDC = (2x)° ⇒ given
∴ 3x + 2x = 120 ⇒ add like terms
∴ 5x = 120 ⇒ divide both sides by 5
∴ x = 24
Column (1) Column (2)
m∠EDF = 120° given
m∠ADB = 3 x given
m∠BDC = 2 x given
∠EDF and ∠ADC are vertical angles defin. of vert. ∠s
∠EDF is congruent to ∠ADC vertical angles are
congruent
m∠ADC = m∠ADB + m∠BDC angle add. post.
m∠EDF = m∠ADC defin. of cong.
m∠EDF = m∠ADB + m∠BDC substitution
120° = 3 x + 2 x substitution
120 = 5 x addition
x = 24 division
∴ The missing reason is " vertical angles are congruent "
- From the explanation above ∠ADC and ∠FDE are vertical
angles then they are congruent according to vertical angle
theorem
