The value of a = ±2
The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this question the coordinates of x are (a - 5, -2a). and the coordinates of y are (a + 1, 2a).
The distance between x and y is 10.
We need to find the value of a.
Using distance formula,
[tex]\Rightarrow 10=\sqrt{((a+1)-(a-5))^2+(2a-(-2a))^2} \\\\\Rightarrow 100=(a+1-a+5)^2+(2a+2a)^2\\\\\Rightarrow 100=6^2+(4a)^2\\\\\Rightarrow 100=36+16a^2\\\\\Rightarrow 64=16a^2\\\\\Rightarrow a^2=4\\\\\Rightarrow a=\pm 2[/tex]
Therefore, the value of a = ±2
Learn more about the distance between two points here:
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