Coordinate Geometry Word Problems Questions Problems

To review these concepts, go to Coordinate Geometry Word Problems Study Guide.

Coordinate Geometry Word Problems Questions Problems

Practice 1

Use the practice set next to test your skill graphing points and naming quadrants.

Problems

Name the quadrant in which each point is located:

(–5,–7)	_____
(4,–2)	_____
(–8,3)	_____
(6,6)	_____

Solutions

(–5,–7)	_____III_____
(4,–2)	_____IV_____
(–8,3)	_____II_____
(6,6)	_____I_____

Practice 2

Problems

1. What is the slope between the points (2,3) and (–3,4)?
2. What is the slope between the points (–3,6) and (–1,–4)?
3. What is the distance between the points (1,2) and (–5,10)?
4. What is the distance between the points (–8,16) and (–3,4)?
5. What is the midpoint between the points (3,5) and (1,3)?
6. What is the midpoint between the points (–4,–2) and (0,6)?

Solutions

1. Read and understand the question. This question is looking for the slope between two points.

Make a plan. Use the formula and substitute the coordinates of the two points. Use (2,3) as (x₁,y₁) and (–3,4) as (x₂,y₂). Carry out the plan. The formula becomes

The slope is –

Check your answer. To check this result, substitute the values in the opposite order to make sure that the slope is the same. The formula is

This result is checking.

2. Read and understand the question. This question is looking for the slope between two points.

Make a plan. Use the formula

and substitute the coordinates of the two points. Use (–3,6) as (x₁,y₁) and (–1,–4) as (x₂,y₂).

Carry out the plan. The formula becomes

The slope is –5.

Check your answer. To check this result, substitute the values in the opposite order to make sure that the slope is the same. The formula is

This result is checking.

3. Read and understand the question. This question is looking for the distance between two points.

Make a plan. Use the formula

and substitute the coordinates of the two points. Use (1,2) as (x₁,y₁) and (–5,10) as (x₂,y₂).

Carry out the plan. The formula becomes

Evaluate the exponents and add the squares together: .

Take the square root of 100 to get a distance of 10 units.

Check your answer. To check this result, substitute the values in the opposite order to make sure that the distance is the same. The formula is

units

This result is checking.

4. Read and understand the question. This question is looking for the distance between two points.

Make a plan. Use the formula

units

and substitute the coordinates of the two points. Use (–8,16) as (x₁,y₁) and (–3,4) as (x₂,y₂).

Carry out the plan. The formula becomes units

Evaluate the exponents and add the squares together: .

Take the square root of 169 to get a distance of 13 units.

Check your answer. To check this result, substitute the values in the opposite order to make sure that the distance is the same. The formula is

units

This result is checking.

5. Read and understand the question. This question is looking for the midpoint between two points.

Make a plan. Use the formula and substitute the coordinates of the two points. Use (3,5) as (x₁,y₁) and (1,3) as (x₂,y₂).

Carry out the plan. The formula becomes . Add to get.

Simplify each fraction to get the midpoint of (2,4).

Check your answer. To check this result, substitute the values in the opposite order to make sure that the midpoint is the same. The formula is

This result is checking.

6. Read and understand the question. This question is looking for the midpoint between two points.

Make a plan. Use the formula and substitute the coordinates of the two points. Use (–4,–2) as (x₁,y₁) and (0,6) as (x₂,y₂).

Carry out the plan. The formula becomes . Add to get . Simplify each fraction to get the midpoint of (–2,2).

Check your answer. To check this result, substitute the values in the opposite order to make sure that the midpoint is the same. The formula is

This result is checking.