Pythagorean theorem and distance Knowledge-Based Practice

Questions

1. 1.

   Which point on the $x$-axis is equidistant from the points $A(-1, 4)$ and $B(6, 3)$?

   • A) $(-2, 0)$
   • B) $(1, 0)$
   • C) $(2, 0)$
   • D) $(4, 0)$
2. 2.

   In the Cartesian coordinate plane, a triangle has vertices at $A(-3, 2)$, $B(1, -1)$, and $C(4, 3)$. What is the geometric classification of triangle $ABC$?

   • A) Scalene right triangle
   • B) Isosceles right triangle
   • C) Acute isosceles triangle
   • D) Obtuse scalene triangle
3. 3.

   A triangle has vertices at $A(-2, 1)$, $B(4, 1)$, and $C(1, 5)$ in the Cartesian coordinate plane. What is the perimeter of triangle $ABC$?

   • A) 14 units
   • B) 16 units
   • C) 18 units
   • D) 22 units
4. 4.

   A point $P(k, 3)$ lies at a distance of 10 units from the point $Q(-2, -5)$ in the Cartesian coordinate plane. If $k > 0$, what is the value of $k$?

   • A) 8
   • B) 6
   • C) 2
   • D) 4
5. 5.

   What is the distance between the points $A(1, -2)$ and $B(6, 10)$ in the Cartesian coordinate plane?

   • A) $\sqrt{89}$
   • B) 17
   • C) $\sqrt{119}$
   • D) 13

Answers and step-by-step solutions appear after you finish the test.