Answer: (-1, 1)
<u>Step-by-step explanation:</u>
Let D represent the fourth vertex with coordinate (x, y)
Since ABCD is a rectangle, then BC || AD and AB || DC
Since BC is parallel to AD, then they have the same slope (m) = -1
Equation of line AD: y - (-2)) = -1(x - 2) ⇒ y + 2 = -x + 2 ⇒ y = -x
Since AB is parallel to DC, then they have the same slope (m) = 1
Equation of line DC: y - 7 = 1(x - 5) ⇒ y - 7 = x - 5 ⇒ y = x + 2
D is where the two lines intersect so the next step is to solve the system of equations: y = -x and y = x + 2
Using substitution method: -x = x + 2 ⇒ -2x = 2 ⇒ x = -1
Now solve for y: y = -x ⇒ y = -(-1) ⇒ y = 1
x = -1 and y = 1
Answer:
The 100th term of the sequence is 503.
Step-by-step explanation:
Given : Sequence 8, 13, 18,23, 28,...
To find : The 100th term in the sequence ?
Solution :
Sequence 8, 13, 18,23, 28,... is the arithmetic sequence
Where, First term is a=8
The common difference is d=13-8=5
The nth term of the sequence is given by
The 100th term is given by,
The 100th term of the sequence is 503.
Answer:
The Proof with Statement and Reason are as follow.
A) Reflexive , SAS , CPCTC.
Step-by-step explanation:
Given:
BA ≅ DC
∠BAC ≅ ∠DCA
To Prove:
BC ≅ DA
Proof:
In ΔBCA and ΔDAC
Statement Reasons
1. BA ≅ DC 1. Given
∠BAC ≅ ∠DCA
2. AC ≅ CA 2. Reflexive Property
3. ΔBCA ≅ ΔDAC 3. S-A-S test
4. BC ≅ DA 4. CPCTC
Answer:
Step-by-step explanation:
1.5