THE MIDPOINT AND DISTANCE FORMULAS WORKSHEET

Problem 1 : 

Find the coordinates of the midpoint of the line segment AB with endpoints A(-2, 3) and B(2, -2).

Problem 2 : 

Find the coordinates of the midpoint of the line segment CD with endpoints C(-2, -1) and D (4, 2).

Problem 3 : 

M is the midpoint of the line segment AB. A has coordinates (-2, 3), and M has coordinates (3/2, 0). Find the coordinates of B.

Problem 4 : 

S is the midpoint of the line segment EF. E has coordinates (2, 2), and S has coordinates (4, -3). Find the coordinates of F.

Problem 5 : 

X is the midpoint of the line segment RT. R has coordinates (-6, -1), and S has coordinates (-1, 1). Find the coordinates of T.

Problem 6 : 

Use the Distance Formula to find the distance, to the nearest hundredth, from A(-2, 3) to B(2, -2).

Problem 7 : 

Use the Distance Formula to find the distance, to the nearest hundredth, from C(3, 2) to D(-3, -1).

Problem 8 : 

Each unit on the map of Lake Okeechobee represents 1 mile. Kemka and her father plan to travel from point A near the town of Okeechobee to point B at Pahokee. To the nearest tenth of a mile, how far do Kemka and her father plan to travel?

Answers

1. Answer :

Write the formula. 

Substitute (-2, 3) for (x₁, y₁) and (2, -2) for (x₂, y₂). 

=  M[⁽⁻² ⁺ ²⁾⁄₂, ⁽³ ⁻ ²⁾⁄₂]

=  M(0, ½)

=  M(0, ½)

The midpoint of the line segment AB is M(0, ½).  

2. Answer :

Write the formula. 

Substitute (-2, -1) for (x₁, y₁) and (4, 2) for (x₂, y₂). 

=  M[⁽⁻² ⁺ ⁴⁾⁄₂, ⁽⁻¹ ⁺ ²⁾⁄₂]

=  M(²⁄₂, ½)

=  M(1, ½)

3. Answer :

Step 1 :

Let the coordinates of B equal (x, y).

Step 2 :

Use the Midpoint Formula.

(3/2, 0)  =  [⁽⁻² ⁺ ˣ⁾⁄₂, ⁽³ ⁺ ʸ⁾⁄₂]

Step 3 :

The coordinates of B are (5, –3).

4. Answer :

Step 1 :

Let the coordinates of B equal (a, b).

Step 2 :

Use the Midpoint Formula.

(4, -3)  =  [⁽² ⁺ ᵃ⁾⁄₂, ⁽² ⁺ ^b⁾⁄₂]

Step 2 :

The coordinates of F are (6, –8).

5. Answer :

Step 1 :

Let the coordinates of T equal (p, q).

Step 2 :

Use the Midpoint Formula.

(-1, 1)  =  [⁽⁻⁶ ⁺ ᵖ⁾⁄₂, ⁽⁻¹ ⁺ ^q⁾⁄₂]

Step 2 :

The coordinates of T are (4, 3).

6. Answer :

Distance Formula : 

d  =  √[(x₂ - x₁)² + (y₂ - y₁)²]

Substitute (-2, 3) for (x₁, y₁) and (2, -2) for (x₂, y₂). 

d  =  √[(2 + 2)² + (-2 - 3)²]

Simplify. 

d  =  √[4² + (-5)²]

d  =  √[16 + 25]

d  =  √41

d  ≈  6.40

The distance between from A(-2, 3) to B(2, -2) is about 6.40 units. 

7. Answer :

Distance Formula : 

d  =  √[(x₂ - x₁)² + (y₂ - y₁)²]

Substitute (3, 2) for (x₁, y₁) and (-3, -1) for (x₂, y₂). 

d  =  √[(-3 - 3)² + (-1 - 2)²]

Simplify. 

d  =  √[(-6)² + (-3)²]

d  =  √[36 + 9]

d  =  √45

d  ≈  6.71

The distance between from C(3, 2) to D(-3, -1) is about 6.71 units. 

8. Answer :

Distance Formula : 

d  =  √[(x₂ - x₁)² + (y₂ - y₁)²]

Substitute (33, 13) for (x₁, y₁) and (22, 39) for (x₂, y₂). 

d  =  √[(33 - 22)² + (13 - 39)²]

Simplify. 

d  =  √[11² + (-26)²]

d  =  √[121 + 676]

d  =  √797

d  ≈  28.2

Kemka and her father plan to travel about 28.2 miles.

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