The distance betwen points A = 1 + 1i and B = a + b is 5. Find the point B for each value provided below.
1 answer:
Answer:
(a) 4+5i or, 4-3i
(b) 1+6i
Step-by-step explanation:
The distance between the points A= 1+i, and B=a+bi is 5.
Therefore, we can write
⇒ ..... (1)
(a) If the value of a is 4, then from equation (1), we get
(4-1)²+(b-1)² = 25
⇒ (b-1)² =16
⇒ b-1 =±4
⇒ b= 5 or -3
Therefore, the point B will be represented by 4+5i or, 4-3i (Answer)
(b) If the value of b is 6, then from equation (1), we get
(a-1)²+(6-1)² = 25
⇒ (a-1)² =0
⇒ a = 1
Therefore, the point B will be represented by 1+6i. (Answer)
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<h2>Kelly is wrong, with this congruent parts, we can conclude that triangles are congruent.</h2>Step-by-step explanation:
To demonstrate congruent triangles, we need to use the proper postulates. There are at least 5 postulates we can use.
- Angle-Angle-Side Theorem (AAS theorem).
- Hypotenuse-Leg Theorem (HL theorem).
- Side-Side-Side Postulate (SSS postulate).
- Angle-Side-Angle Postulate (ASA postulate).
- Side-Angle-Side Postulate (SAS postulate).
In this case, Kelly SAS postulate, because the corresponding sides-angles-sides are congruent, i.e., KL ≅ MN and LM ≅ KN, also, all corresponding angles are congruent.
So, as you can see, only using SAS postulate, the congruency can be demonstrated. (Refer to the image attached to see an example of SAS postulate)
