Question 1

Given the points $$(1, 3)$$ and $$(2, 5)$$, what is the exact distance between them?

Accepted Answer

$$\sqrt{2}$$

Question 2

Find the distance between the points $$(-1, 6)$$ and $$(-11, 2).$$

Accepted Answer

$$\sqrt{104}$$

Question 3

What is the distance between the points $$(12, 5)$$ and $$(12, \frac{3}{2})$$?

Accepted Answer

$$\frac{7}{2}$$

Question 4

A triangle has legs of length $$3$$ and $$4. $$What is the length of the hypotenuse?

Accepted Answer

$$5$$

Question 5

Find the midpoint of the segment joining $$A = (1, 2)$$ and $$B = (11, 3).$$

Accepted Answer

$$(6, 2.5)$$

Question 6

Find the midpoint of the segment joining $$A = (-5, 2)$$ and $$B = (-4, -1).$$

Accepted Answer

$$(-4.5, 0.5)$$

Question 7

A line segment $$AB$$ has midpoint $$M = (2, 5)$$ and endpoint $$A = (1, 1). $$What are the coordinates of endpoint $$B$$?

Accepted Answer

$$(3, 9)$$

Question 8

A city park is represented by the points $$(2, 3)$$ and $$(8, 9) on a $$map. What is the exact length of the diagonal across the park?

Accepted Answer

$$\sqrt{72}$$

Question 9

If the midpoint of a segment is $$(0, 0)$$ and one endpoint is $$(-2, 4)$$, what are the coordinates of the other endpoint?

Accepted Answer

$$(2, -4)$$

Question 10

A hiking trail starts at $$(5, 7)$$ and ends at $$(13, 15). $$What is the midpoint of the trail?

Accepted Answer

$$(9, 11)$$

Question 11

A rectangle has vertices at $$(0, 0)$$ and $$(6, 8). $$What is the length of the diagonal?

Accepted Answer

$$10$$

Question 12

If the endpoints of a segment are $$(a, b)$$ and $$(c, d)$$, what is the formula for the midpoint?

Accepted Answer

$$\left( \frac{a+c}{2}, \frac{b+d}{2} \right)$$

Question 13

If the endpoints of a segment are $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$, what is the formula for the distance between them?

Accepted Answer

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

Question 14

A drone flies from $$(4, 2) to$$ $$(10, 8). $$What is the straight-line distance it travels?

Accepted Answer

$$6\sqrt{2}$$

Question 15

A segment has endpoints $$(x, y)$$ and $$(x, y + h). $$What is the distance between the endpoints?

Accepted Answer

$$|h|$$

Question 16

A segment has endpoints $$(a, b)$$ and $$(a, d). $$What is the midpoint?

Accepted Answer

$$(a, \frac{b+d}{2})$$

Question 17

A segment has endpoints $$(x_1$, y_1$)$$ and $$(x_2$, y_2$). If $$the midpoint is $$(m_x, m_y)$$, what is the formula for the coordinates of $$x_2$$ and $$y_2$$ given $$x_1$$, $$y_1$$, m_x, m_y$$?

Accepted Answer

$$(2m_x - x_1$, 2m_y - y_1$)$$

Question 18

A segment has endpoints $$(0, 0)$$ and $$(a, b). $$What is the distance between the endpoints?

Accepted Answer

$$\sqrt{a^2$ + b^2$}$$

Question 19

A segment has endpoints $$(x_1$, y_1$)$$ and $$(x_2$, y_2$). If$$ $$x_1$$ = $$x_2$$, what is the distance between the endpoints?

Accepted Answer

$$|y_2$ - y_1$|$$

Question 20

A segment has endpoints $$(x_1$, y_1$)$$ and $$(x_2$, y_2$). If$$ $$y_1$$ = $$y_2$$, what is the distance between the endpoints?

Accepted Answer

$$|x_2$ - x_1$|$$

Distance and Midpoint Formulas – Precalculus Study Guidance

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