Question

the coordinate plane shows the points x, y and z.
for a, enter the distance from point point x and point y?
for b, enter the distance from point point x and point z?

Explanation:

Step1: Determine coordinates of points

First, we need to find the coordinates of points \( X \), \( Y \), and \( Z \). From the graph:

• Point \( Y \) is at \( (0, -4) \) (since it's on the y - axis, x - coordinate is 0 and y - coordinate is - 4).
• Point \( X \) is at \( (2, - 4) \) (x - coordinate is 2, y - coordinate is - 4).
• Point \( Z \) is at \( (2, - 3) \) (x - coordinate is 2, y - coordinate is - 3).

Step2: Calculate distance between X and Y

The distance formula between two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). But when the y - coordinates are the same (horizontal line), the distance is \( |x_2 - x_1| \). For points \( X(2,-4) \) and \( Y(0,-4) \), \( y_1 = y_2=-4 \). So the distance \( d_{XY}=|2 - 0|=2 \).

Step3: Calculate distance between X and Z

When the x - coordinates are the same (vertical line), the distance is \( |y_2 - y_1| \). For points \( X(2,-4) \) and \( Z(2,-3) \), \( x_1 = x_2 = 2 \). So the distance \( d_{XZ}=|-3-(-4)|=|-3 + 4| = 1 \).

Answer:

(for A and B):
A (distance between X and Y): \( 2 \)
B (distance between X and Z): \( 1 \)