Question

If (a, a) is equidistant from the points (-1, 3) and (2, -4), find the value of a.

• A. 1.25
• B. -1.25
• C. 2.5
• D. -2.5

Answer 1

The correct option is B -1.25

Let A(a, a), B(-1, 3), and C(2, -4)

The distance between two points $(x_1,y_1)\text{and}(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}.$

AB = AC

$\sqrt{(-1-a{)}^2+(3-a{)}^2}=\sqrt{(2-a{)}^2+(-4-a{)}^2}$
$(-1-a{)}^2+(3-a{)}^2=(2-a{)}^2+(-4-a{)}^2$
$(1+a{)}^2+(3-a{)}^2=(2-a{)}^2+(4+a{)}^2$
$1+2a+a^2+9-6a+a^2=4-4a+a^2+16+8a+a^2$
10 - 4a = 20 + 4a
8a = -10
a = -1.25