Question

If the coordinates of A are (3, 4) and the coordinates of B are (-3,-4), then the length of AB is ·

Answer 1

the Points A and B are two points on the cartesian coordinate system.

To find their distances apart, they are considered as the vertices of a right angled triangle and their distance will then the length of the hypothenuse. Given mathematically as:

`\text{Distance, D = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}^{}`

where we can then regard (3,4) as point 2 and (-3,-4) as point 1.

`\begin{gathered} \text{Distance, D = }\sqrt[]{(4_{}-(-4)_{})^2+(3_{}-(-3)_{})^2}^{} \\ \text{Distance, D = }\sqrt[]{(8_{})^2+(6_{})^2}^{} \\ \text{Distance, D = }\sqrt[]{64^{}+36^{}} \\ \text{Distance, D = }\sqrt[]{100}=10 \end{gathered}`

Therefore, the distance between the points is 10 units.