Question

The distance between (a, -1) and (3, 2) is 5. Classify if each of the following numbers are possible values of a:

a) a= -1
b) a= 3
c) a= 4
d) a= 7
e) a= 8

Answer 1

The value of a that satisfies the given condition is a = 7. The correct answer is d) a= 7.

Step-by-step explanation:

To find the distance between two points (a, -1) and (3, 2) in a Cartesian plane, we use the distance formula: √((x2 - x1)^2 + (y2 - y1)^2).

Here, x1 = a, y1 = -1, x2 = 3, and y2 = 2.

Given that the distance between these points is 5, we can calculate the distance using the formula:

Distance = √((3 - a)^2 + (2 - (-1))^2) = 5

Squaring both sides of the equation to eliminate the square root gives us:

(3 - a)^2 + 3^2 = 25

(3 - a)^2 + 9 = 25

(3 - a)^2 = 25 - 9

(3 - a)^2 = 16

Taking the square root of both sides gives us two possible solutions:

3 - a = ±√16

3 - a = ±4

Solving for 'a' in both cases:

When 3 - a = 4:

a = 3 - 4

a = -1

When 3 - a = -4:

a = 3 + 4

When 3 - a = -4:

a = 7

Therefore, the possible values for 'a' are a = -1 and a = 7.

Hence, the possible values of 'a' that satisfy the given condition are a = 4, a = 7, and a = 8.

These values make the distance between the points (a, -1) and (3, 2) equal to 5 units.

Answer 2

To find the distance between two points (a, -1) and (3, 2) in a Cartesian plane.

a) a = 4

b) a = 7

c) a = 8

Step-by-step explanation:

To find the distance between two points (a, -1) and (3, 2) in a Cartesian plane, we use the distance formula: √((x2 - x1)^2 + (y2 - y1)^2). Here, x1 = a, y1 = -1, x2 = 3, and y2 = 2.

Given that the distance between these points is 5, we can calculate the distance using the formula:

Distance = √((3 - a)^2 + (2 - (-1))^2) = 5

Squaring both sides of the equation to eliminate the square root gives us:

(3 - a)^2 + 3^2 = 25

(3 - a)^2 + 9 = 25

(3 - a)^2 = 25 - 9

(3 - a)^2 = 16

Taking the square root of both sides gives us two possible solutions:

3 - a = ±√16

3 - a = ±4

Solving for 'a' in both cases:

When 3 - a = 4:

a = 3 - 4

a = -1

When 3 - a = -4:

a = 3 + 4

a = 7

Therefore, the possible values for 'a' are a = -1 and a = 7.

Hence, the possible values of 'a' that satisfy the given condition are a = 4, a = 7, and a = 8. These values make the distance between the points (a, -1) and (3, 2) equal to 5 units.