Answer:
3.x = -3 or x =5.
4.y = -4 or y=12.
Explanation:
3. Use the distance formula to find the value of x if the distance between (1, 2) and (x, 5) is 5units.
The distance formula is:

where:
d is the distance between the two points
are the coordinates of the first point
) are the coordinates of the second point
In this case, we have:
d = 5


`Substituting these values into the distance formula, we get:

squaring both side





Factoring the quadratic, we get:


x(x-5)+3(x-5)=0
(x-5)(x+3)=0
either x=5
or x=-3
Therefore, x = -3 or x =5.
4. Use the distance (-1, 4) and (5, y) is 10 units.
The distance formula is the same as in the previous problem. In this case, we have:
d = 10


Substituting these values into the distance formula, we get:


squaring both sides
100 = 36 + (y - 4)²
100-36=(y-4)²
64 = (y - 4)²
±8 = y - 4
taking positive
8=y-4
y=8+4
y=12
again
taking negative
-8=y-4
y = -8+4
y = -4
Therefore, y = -4 or y=12.