Determine Distance on the Coordinate Plane
Name Period
Objectives / Objetivos
Content Objective: I can find the distance between two points on the coordinate plane using absolute value.
Language Objective: I can explain my work using the words distance, absolute value, horizontal distance, and vertical distance.
Key Idea / Idea clave
Distance on the Coordinate Plane. Formula: Distance = |x1 − x2| (horizontal) or |y1 − y2| (vertical). 1. Same quadrant / Same sign: Subtract absolute values of differing coordinates. 2. Different quadrants / Opposite signs: Add absolute values of differing coordinates. 3. Distance is never negative; it is zero when both points coincide
I Notice / Observo
- What do the two points (-3, 2) and (4, 2) have in common?
- How can you count the distance between points in the same row?
I Wonder / Me pregunto
- What if the two points are NOT in the same row or column?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Distance on the Coordinate Plane Distancia en el plano de coordenadas | The nonnegative distance between points, found from the absolute difference of coordinates on a horizontal or vertical line. La distancia no negativa entre puntos, que se halla con la diferencia absoluta de las coordenadas en una línea horizontal o vertical. |
| Distance Distancia | How far apart two points are. It is never negative. Qué tan separados están dos puntos. Nunca es negativo. |
| Absolute value Valor absoluto | How far a number is from zero. It is never negative. Qué tan lejos está un número de cero. Nunca es negativo. |
| Horizontal distance Distancia horizontal | How far apart two points are going left or right. Qué tan separados están dos puntos yendo a la izquierda o a la derecha. |
| Vertical distance Distancia vertical | How far apart two points are going up or down. Qué tan separados están dos puntos yendo hacia arriba o hacia abajo. |
| Coordinate plane Plano cartesiano | A grid with a line going across and a line going up to plot points. Una cuadrícula con una línea horizontal y una vertical para marcar puntos. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. What is the distance between (-4, 3) and (2, 3)?
- A 2 units
- B 4 units
- C 6 units
- D 8 units
Answer:
2. Plot these pairs and find each distance: A(-5, 3) to B(2, 3), and C(4, -2) to D(4, 4)
- A: (-5, 3)
- B: (2, 3)
- C: (4, -2)
- D: (4, 4)
3. Find the perimeter of each rectangle using its vertex coordinates.
Complete each empty cell. Show your reasoning below.
| Rectangle | Vertices | Width | Height | Perimeter |
|---|---|---|---|---|
| Rect 1 | (-3, 1), (4, 1), (4, 5), (-3, 5) | |||
| Rect 2 | (-2, -4), (6, -4), (6, 2), (-2, 2) |
4. Find the Distance Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: