Draw the image of triangle A1,B1,C1 of triangle ABC under the reflection in the x= 0 Where A= A1 B= B1 C= C1

Question

ScanSolve AI Tutor · Accepted Answer

Let's reflect triangle ABC across the line $x=0$ (which is the y-axis) to find triangle A1B1C1.

Determine the rule for reflection in the line $x=0$ .
A reflection in the y-axis (the line $x=0$ ) transforms a point $(x,y)$ to $(-x,y)$ .
Apply the reflection rule to the vertices of triangle ABC.
- For $A(3,5)$ :
$A_1 = (-3, 5)$
- For $B(0,2)$ :
$B_1 = (-0, 2) = (0, 2)$
- For $C(5,1)$ :
$C_1 = (-5, 1)$
So, the vertices of the image triangle are $A_1(-3,5)$ , $B_1(0,2)$ , and $C_1(-5,1)$ . Note that $B_1$ is the same as $B$ because $B$ lies on the line of reflection ( $x=0$ ).
Plot the image points on your graph.
- Plot $A_1(-3,5)$ : Move 3 units left from the origin, then 5 units up. Label it $A_1(-3,5)$ .
- Plot $B_1(0,2)$ : This is the same point as $B$ . Label it $B_1(0,2)$ .
- Plot $C_1(-5,1)$ : Move 5 units left from the origin, then 1 unit up. Label it $C_1(-5,1)$ .
Draw triangle $A_1B_1C_1$ .
Connect the points $A_1$ , $B_1$ , and $C_1$ with straight lines to form the reflected triangle.

You have now drawn the image of triangle ABC under reflection in the line $x=0$ .

Step-by-step solution