Ok I really need help with this problem?

Question

ok I have this Geometry problem thats says use the distance formula to decide whether PQ is congruent to QR but they gave me three corrdinates they are P(-4,3) Q (-2,1), R(0,-1)

Now I was pretty sure that there are only two cordinates used when finding the distance between them but I so confused what do I do with the 3rd one HELPPPPP MEE PLEASE

Oh and if you could show me how you did this problem then that would help alot to

Answer 1

You are right. Two coordinates are used to find the distance.
Find the distance between P and Q.
Find the distance between Q and R.
If the two distances are equal, then PQ is congruent to QR.
For example, the distance between P and Q is
d = sqrt[(-4-(-2))^2 + (3-1)^2]
= sqrt[(-2)^2 + 2^2]
= sqrt(4 + 4)
= sqrt(8)
= 2sqrt(2)
Now, you calculate the distance between Q and R (you should get the same result, 2sqrt(2)).

Answer 2

Recall that the distance formula is

d = sqrt ( (x2 - x1)^2 + (y2 - y1)^2 )

Now, you must find the length of PQ and QR.

Since PQ uses the points (-4, 3) and (-2, 1), we plug this in for (x1, y1) and (x2, y2) respectively.

PQ = sqrt ( (-2 - (-4))^2 + (1 - 3)^2 )
PQ = sqrt ( (2)^2 + (-2)^2 )
PQ = sqrt (4 + 4) = sqrt(8)

QR uses the points (-2, 1) and (0, -1), so we do the same thing.

QR = sqrt ( (0 - (-2))^2 + (-1 - 1)^2 )
QR = sqrt ( (2)^2 + (-2)^2)
QR = sqrt (4 + 4)
QR = sqrt(8)

As you can see, the length of PQ is equal to the length of QR (they're both equal to sqrt(8)). Therefore, they are congruent.

Answer 3

PQ is the segment between p(-4,3) & Q(-2,1) & is
PQ=√((-4--2)^2+(3-1)^2)
PQ=√(4+4)=√8=2√2

QR is the segment betweeb Q(-2,1) & R(0,-1) & is
QR=√((-2-0)^2+(-1-1)^2=√(4+4)=√8
QR=2√2
PQ=2√2
they are congruent.

Answer 4

sqr[(y2-y1)²+(x2-x1)²]
plug in numbers to find out.