What is the distance between point P(–2, 1, 3) and point Q(–1, 4, –2) to the nearest tenth? ?

Question

What is the distance between point P(–2, 1, 3) and point Q(–1, 4, –2) to the nearest tenth?

35.1 units

18.4 units

9.3 units

5.9 units

2. If A(2, 0, –1), B(–1, 2, –3), C(0, 4, –2), and D(3, –1, 1) are points in a three-dimensional coordinate system, which segment is longest?

segment AB

segment BC

segment CD

segment DA

3. What are the coordinates of the midpoint of the segment joining A(2, –3, 1) and Z(–6, 3, 1)?

(–4, 3, 0)

(8, 6, 0)

(–4, 0, 2)

(–2, 0, 1)

4. If points P(6, 0, 4), Q(3, 2, 1), and R are collinear such that PQ = QR, which of the following are the coordinates of point R?

(0, 4, –2)

(–3, 2, –3)

(1, –2, 0)

(4, 1, –3)

Answer 1

You faked me out.  This is the geography section.  I gave the answers thinking this was the math section.  You're lucky I didn't realize this before I did the answers.

1.

P(–2, 1, 3) and point Q(–1, 4, –2)

x = 1, y = 3, z = 5

d = (1^2 + 3^2 + 5^2)^-2

d = (35)^-2

d = 5.9

2.

A(2, 0, –1), B(–1, 2, –3), C(0, 4, –2), and D(3, –1, 1)

AB = (3^2 + 2^2 + 2^2)^-2 = (17)^-2

BC = (1^2 + 2^2 + 1^2)^-2 = (6)^-2

CD = (3^2 + 5^2 + 3^2)^-2 = (43)^-2

DA = (1^2 + 1^2 + 2^2)^-2 = (60^-2

CD is the longest

3.

A(2, –3, 1) and Z(–6, 3, 1)

x = 8/2 - 6 = -2

y = 6/2 - 3 = 0

z = 0 + 1 = 1

M(-2, 0, 1)

4.  

P(6, 0, 4), Q(3, 2, 1), and R are collinear such that PQ = QR

PQ = (3^2 + 2^2 + 3^2)^-2 = (22)^-2

If R(0, 4, -2)

QR = (3^2 + 2^2 + 3^2)^-2 = (22)^-2

If R(-3, 2, -3)

QR = (6^2 + 0 + 4^2)^-2 = (44)^-2

If R(1, -2, 0)

QR = (2^2 + 4^2 + 1)^-2 = (21)^-2

If R(4, 1, -3)

QR = (1 + 1 + 4^2)^-2 = (18)^-2

Therefore, R(0, 4, -2)