Question 1

Given points $$P(1,5)$$ and $$Q(1,10)$$, what is the distance between $$P$$ and $$Q$$?

Accepted Answer

$$5$$

Question 2

What are the coordinates of the midpoint of the segment joining $$P(1,5)$$ and $$Q(1,10)$$?

Accepted Answer

$$(1,7.5)$$

Question 3

Find the distance between the points $$P(4,1)$$ and $$Q(6,5.5). $$Give your answer in simplest radical form.

Accepted Answer

$$\sqrt{26}$$

Question 4

What are the coordinates of the midpoint of the segment joining $$P(4,1)$$ and $$Q(6,5.5)$$?

Accepted Answer

$$(5,3.25)$$

Question 5

Given $$P(\sqrt{3},8)$$ and $$Q(\sqrt{3},10)$$, what is the distance between $$P$$ and $$Q$$?

Accepted Answer

$$2$$

Question 6

What are the coordinates of the midpoint of the segment joining $$P(\sqrt{3},8)$$ and $$Q(\sqrt{3},10)$$?

Accepted Answer

$$(\sqrt{3},9)$$

Question 7

Determine whether the points $$P(0,0)$$, $$Q(4,7)$$, and $$R=(-4,-7)$$ are collinear.

Accepted Answer

Yes, because $$d(P,Q) + d(Q,R) = d(P,R)$$

Question 8

Find the point on the $$y-$$axis that is equidistant from the points $$(-2,0)$$ and $$(1,3).$$

Accepted Answer

$$(0,1)$$

Question 9

In 1985, Americans spent $$8$$ billion dollars on a commodity. In 1996, they spent $$146$$ billion. Assuming a linear trend, estimate the amount spent in 1988.

Accepted Answer

$$38$$ billion

Question 10

Let $$A(2,1)$$, $$B(7,8)$$, and $$C(3,10) be $$three points. Find the coordinates of point $$D so $$that $$A$$, $$B$$, $$C$$, $$D$$ form a parallelogram with $$AC as $$one of the diagonals.

Accepted Answer

$$(8, -1)$$

Question 11

Let $$A(2,1)$$, $$B(7,8)$$, and $$C(3,10) be $$three points. Find the coordinates of point $$D so $$that $$A$$, $$B$$, $$C$$, $$D$$ form a parallelogram with $$BC as $$one of the diagonals.

Accepted Answer

(-2, 5)$

Question 12

Let $$A(2,1)$$, $$B(7,8)$$, and $$C(3,10) be $$three points. Find the coordinates of point $$D so $$that $$A$$, $$B$$, $$C$$, $$D$$ form a parallelogram with $$AB as $$one of the diagonals.

Accepted Answer

$$(8, 3)$$

Question 13

Given that $$(3,5)$$, $$(7,8)$$, $$(x,13)$$, and $$(7,10)$$ are the vertices of a parallelogram, find $$x.$$

Accepted Answer

$$11$$

Question 14

A city is planning to build a new park that is equidistant from the schools at $$(2,0)$$ and $$(8,6). If $$the park must be located on the $$x-$$axis, what are its possible coordinates?

Accepted Answer

$$(5,0)$$

Question 15

Which of the following is the correct formula for the distance between points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$-x_1$)^2$$ + ($$y_2$$-$$y_1)^2$}$$

Question 16

A cell phone tower is located at $$(0,0). A $$user is at $$(6,8). $$What is the distance between the user and the tower?

Accepted Answer

$$10$$

Question 17

A delivery drone must fly from warehouse $$A(2,3) to $$customer $$B(8,15). $$What is the straight-line distance the drone must travel?

Accepted Answer

$$13.416$$

Question 18

Which of the following is the correct formula for the midpoint of the segment joining $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$)$$?

Accepted Answer

$$\left( \frac{x_1$+x_2$}{2}, \frac{y_1$+y_2$}{2} \right)$$

Coordinate Geometry: Distance, Midpoint, Collinearity, and Parallelograms

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