Coordinates of a point is (0, 1) and ordinate of an another point is -3. If distance between both the points is 5, then abscissa of second point is

Options

A. 3
B. -3
C. `pm`3
D. 1

Answer

To solve the problem, we need to find the abscissa (x-coordinate) of the second point given the following information:

1. The coordinates of the first point are (0, 1).
2. The ordinate (y-coordinate) of the second point is -3.
3. The distance between the two points is 5.

Let’s denote the coordinates of the second point as (x, -3), where x is the abscissa we need to find.

### Step-by-Step Solution:

**Step 1: Write down the distance formula.**
The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

**Step 2: Assign the coordinates.**
For our points:
- First point \((x_1, y_1) = (0, 1)\)
- Second point \((x_2, y_2) = (x, -3)\)

**Step 3: Substitute the coordinates into the distance formula.**
Given that the distance \( d = 5 \), we substitute the coordinates into the distance formula:
\[ 5 = \sqrt{(x - 0)^2 + (-3 - 1)^2} \]

**Step 4: Simplify the equation.**
This simplifies to:
\[ 5 = \sqrt{x^2 + (-4)^2} \]
\[ 5 = \sqrt{x^2 + 16} \]

**Step 5: Square both sides to eliminate the square root.**
Squaring both sides gives:
\[ 25 = x^2 + 16 \]

**Step 6: Solve for \( x^2 \).**
Subtract 16 from both sides:
\[ 25 - 16 = x^2 \]
\[ 9 = x^2 \]

**Step 7: Take the square root of both sides.**
Taking the square root gives:
\[ x = 3 \quad \text{or} \quad x = -3 \]

Thus, the abscissa of the second point can be either 3 or -3.

### Final Answer:
The abscissa of the second point is either \( 3 \) or \( -3 \).

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