Question

3
ivy will rotate abc using the rule (x, y) → (-x, -y).
statement\tt/f?
the location of c’ will be (-2, 5).\tt
ivy will rotate the triangle 180°.\t
triangle a’b’c’ will be in quadrant i.\t
rewrite the false statement to make it true:

(other parts with coordinates like m(6,8), n(1,2), o(1,8) and their images, and a rectangle rotation problem are partially visible but the main triangle rotation problem is as above.)

Explanation:

Step1: Find coordinates of point C

From the graph, point C has coordinates \((-2, 5)\) (assuming the grid is such that we identify the x and y values; looking at the grid, x - coordinate is -2, y - coordinate is 5).

Step2: Apply the rotation rule \((x,y)\to(-x,-y)\)

For point C \((x = - 2,y = 5)\), substituting into the rule:
\(x'=-(-2)=2\)
\(y'=-5\)
So the coordinates of \(C'\) should be \((2, - 5)\), not \((-2,5)\). So the statement "The location of \(C'\) will be \((-2,5)\)" is false. To make it true, we rewrite it as "The location of \(C'\) will be \((2, - 5)\)".

Step3: Analyze the rotation angle and quadrant

The rule \((x,y)\to(-x,-y)\) is the rule for a \(180^{\circ}\) rotation (either clockwise or counter - clockwise, as \(180^{\circ}\) rotation has the same rule for both directions). So the statement "Ivy will rotate the triangle \(180^{\circ}\)" is true.

For the statement "Triangle \(A'B'C'\) will be in quadrant I", after rotation, let's find coordinates of A and B. Let's assume point A is \((-2,-1)\) (from the graph), applying the rule \((x,y)\to(-x,-y)\), \(A'\) will be \((2,1)\). Point B: let's assume B is \((-5,5)\), then \(B'\) will be \((5, - 5)\). Point \(C'\) is \((2,-5)\). So the triangle \(A'B'C'\) has points in quadrant I (A') and quadrant IV (B' and C'), so it is not entirely in quadrant I. To make it true, we can rewrite it as "Triangle \(A'B'C'\) will be in quadrant I and IV" (or other correct description based on the actual coordinates). But since the main false statement here (from the first one we analyzed) is about the location of \(C'\), we focus on that.

Answer:

• False statement: "The location of \(C'\) will be \((-2,5)\)"
• Rewritten true statement: "The location of \(C'\) will be \((2, - 5)\)"
• The statement "Ivy will rotate the triangle \(180^{\circ}\)" is true (since the rule \((x,y)\to(-x,-y)\) is for \(180^{\circ}\) rotation).
• For the statement "Triangle \(A'B'C'\) will be in quadrant I", a true rewrite could be "Triangle \(A'B'C'\) will have vertices in quadrant I and quadrant IV" (or based on exact coordinates of A, B, C from the graph).