Question

From the following graph, find the co-ordinates of the point(s) satisfying the given condition.

1. the abscissa is 4
2. the ordinate is –4
3. the ordinate is 6
4. the abscissa is –3
5. the abscissa and ordinate are equal but opposite in sign.
6. the points whose abscissa are equal but ordinate are equal and opposite.

Answer 1

a. The abscissa is 4

Given: Abscissa (x = 4)

Step-wise calculation:

1. Look on the graph for the point(s) whose (x)-coordinate is (4).

2. Point (A) lies on the (x)-axis at (x = 4), so A = (4, 0).

b. The ordinate is (–4)

Given: Ordinate (y = –4)

Step-wise calculation:

1. Look for point(s) on the horizontal line (y = –4).

2. Point (F) is on the (y)-axis at (y = –4), so F = (0, –4).

c. The ordinate is 6

Given: Ordinate (y = 6)

Step-wise calculation:

1. Look for point(s) on the horizontal line (y = 6).

2. Point (H) is at (y = 6) and (x = 8), so H = (8, 6).

d. The abscissa is (–3)

Given: Abscissa (x = –3)

Step-wise calculation:

1. Look for point(s) on the vertical line (x = –3).

2. Point (E) lies at (x = –3) and (y = –6), so E = (–3, –6).

e. The abscissa and ordinate are equal but opposite in sign (x = –y)

Given: Abscissa and ordinate equal but opposite in sign x = –y or y = –x.

Step-wise calculation:

1. Check plotted points where (y = –x).

2. Point (C) is (–4, 4) and satisfies 4 = – (–4).

f. The points whose abscissa are equal but ordinate are equal and opposite (x₁ = x₂, ; y₁ = –y₂)

Given: Two points with x₁ = x₂, y₁ = –y₂.

Step-wise calculation:

1. Look for two points directly above/below each other same (x) and symmetric about the x-axis, opposite y.

2. Points B = (2, 4) and G = (2, –3) do not match ordinates not opposite.

3. Points D = (–5, –3) and C = (–4, 4) do not match abscissae not equal.

4. No visible pair of labeled points has the same (x) with ordinates equal in magnitude and opposite in sign.