FIRST QUESTION
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula =
Now, plug the values into the formula, So,
distance =
=
=
=
=
=
So, the length of AB is.
<span>THIRD QUESTION
</span>Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.
Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint =
Now, equaling the ordered pair, we have,
.............equation (1)
................equation (2)
Now, taking equation (1)
Now, taking equation (2)
<span>So, the co ordinates of C are (a, b) which is <u>(-1 , 4)
</u></span>
<span>SECOND QUESTION:
</span>Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1
Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4
So, x=1 and y=4
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula =
Now, plug the values into the formula, So,
distance =
=
=
=
=
=
So, the length of AB is
<span>THIRD QUESTION
</span>Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.
Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint =
Now, equaling the ordered pair, we have,
Now, taking equation (1)
Now, taking equation (2)
<span>So, the co ordinates of C are (a, b) which is <u>(-1 , 4)
</u></span>
<span>SECOND QUESTION:
</span>Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1
Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4
So, x=1 and y=4
