Question

quadrilateral ABCD shown on coordinate plane with coordinates at 1 comma 2, 2 comma 3, 4 comma 2, and 2 comma 1 Quadrilateral ABCD is dilated by a scale factor of 1 over 2 centered around (2, 2). Which statement is true about the dilation? segment B prime D prime will run through (2, 2) and will be shorter than segment BD. segment B prime D prime will run through (2, 2) and will be longer than segment BD. segment B prime D prime will parallel to segment BD and will be shorter than segment BD. segment B prime D prime will be parallel to segment BD and will be longer than segment BD.

Answer 1

Answer:

segment B'D' runs through O(2, 2) and is shorter than segment BD.

Step-by-step explanation:

Given quadrilateral ABCD with vertices A(1,2), B(2,3), C(4,2) and D(2,1).

The dilation with center at point O(2,2) and coefficient of dilation $\frac{1}{2}$ has the rule

$(x,y)\rightarrow \left(\dfrac{1}{2}(x-2)+2,\dfrac{1}{2}(y-2)+2\right)$

So,

• $A(1,2)\rightarrow A'(1.5,2)$
• $B(2,3)\rightarrow A'(2,2.5)$
• $C(4,2)\rightarrow C'(3,2)$
• $D(2,1)\rightarrow D'(2,1.5)$

As you can see, segment B'D' runs through O(2, 2) and is shorter than segment BD.

Segments B'D' and BD lie on the same line.