14. Write down the coordinates of point A and point B on the diagram - Junior Cycle Mathematics - Question 14 - 2012

Point D is marked at (6, 8) on the diagram.

To find the midpoint C of segment AB, use the midpoint formula:

$ext{Midpoint} = \left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right)$

Thus,

$\text{C} = \left( \frac{1+1}{2}, \frac{1+11}{2} \right) = \left( 1, 6 \right).$

Draw lines connecting points A to D, B to D, and C to D on the diagram.

To find the lengths of |AD| and |BD|, use the distance formula:

$|AD| = \sqrt{(6-1)^2 + (8-1)^2} = \sqrt{25 + 49} = \sqrt{74}$

and

$|BD| = \sqrt{(6-1)^2 + (8-11)^2} = \sqrt{25 + 9} = \sqrt{34}.$

Type: Isosceles.

Reason: Two sides are the same length, as calculated from step (e).

Answer: Yes, they are congruent.

Reason: By SSS criterion, as follows:

• AC = BC
• AD = BD
• CD = CD