Coordinate geometry (distance, midpoint, slopes) Knowledge-Based Practice

Questions

1. 1.

   In the coordinate plane, what is the y-intercept of the perpendicular bisector of the line segment joining points $A(-4, 2)$ and $B(2, 8)$?

   • A) -1
   • B) 2
   • C) 4
   • D) 6
2. 2.

   The points $A(-5, -2)$, $B(1, k)$, and $C(4, 10)$ lie on the same straight line in the coordinate plane. What is the value of $k$?

   • A) 6
   • B) 4
   • C) 8
   • D) -10
3. 3.

   The points $A(1, 2)$, $B(7, 2)$, and $C(4, k)$ are the vertices of an isosceles triangle such that the lengths of sides $AC$ and $BC$ are both equal to 5 units. If $k > 2$, what is the value of $k$?

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

   In the coordinate plane, the line segment joining points $A(-3, 1)$ and $B(5, 7)$ is perpendicular to the line passing through points $C(2, -4)$ and $D(k, 0)$. What is the value of $k$?

   • A) 5
   • B) 1
   • C) -1
   • D) -5
5. 5.

   In the coordinate plane, point $M$ is the midpoint of the line segment with endpoints $A(-6, 3)$ and $B(4, 7)$. What is the distance between point $M$ and point $C(4, -7)$?

   • A) 11
   • B) 13
   • C) 15
   • D) 17

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