Determine Distance on the Coordinate Plane

6.NOS.9 · Unit 7 · Lesson 6

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 represents length, so it is always positive

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 / TérminoDefinition / Definición
Distance on the Coordinate Plane
Distancia en el plano de coordenadas		The positive space between points, found from the absolute difference of coordinates on a horizontal or vertical line.
El espacio positivo 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

  1. What is the distance between (-4, 3) and (2, 3)?
    1. 2 units
    2. 4 units
    3. 6 units
    4. 8 units
  2. Plot these pairs and find each distance: A(-5, 3) to B(2, 3), and C(4, -2) to D(4, 4)
  3. Find the perimeter of each rectangle using its vertex coordinates.
  4. Find the Distance Error
    1. Step 1: Problem — Find the distance between (-3, 4) and (5, 4)
    2. Step 2: Student thinking — Subtract: 5 - 3 = 2
    3. Step 3: Student answer — The distance is 2 units

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: