Question

if D(6,5)and R(2,y) are two points such that DR=5 units find the possible values of y​

Answer 1

Answer:

Distance between the points (-2, -5) and (-6, y)

=(−6+2)2+(y+5)2−−−−−−−−−−−−−−−−−−√=16+y2+10y+25−−−−−−−−−−−−−−−√

=y2+10y+41−−−−−−−−−−−√

Given that,

y2+10y+41−−−−−−−−−−−√=5⇒ y2+10y+41=25

⇒ y2+10y+16=0⇒ y2+2y+8y+16=0

⇒ y(y+2)+8(y+2)=0⇒ (y+2)(y+8)=0

⇒ y+2=0ory+8=0

y=−2ory=−8

Answer 2

Solution: In the given problem, we have: x1 = 1, y1 = 2, x2 = 4, and y2 = 3. Therefore, we have:

q1 = (3-2)² = 1

q2= (4-1)² = 9

distance (d) = √(q1 + q2)

∴d = √(1 + 9) = √10 = 3.16227 units.

As you can see in the previous example, we have written the units of distance as ‘units’, and not ‘square units.’