Question

3 figure j k l m n is reflected across the x - axis to form figure j k l m n. tell whether each statement is true or false. a. l is located at (-3, 4). b. m is located 1 unit below the x - axis. c. the y - coordinate of k is the opposite of the y - coordinate of k. d. the line of reflection is the y - axis. e. nm = nm. f. the x - coordinate of n is the opposite of the x - coordinate of n. g. m∠j = m∠j

Explanation:

To solve this, we use the rule for reflecting a point \((x, y)\) across the \(x\)-axis: the image is \((x, -y)\) (the \(x\)-coordinate stays the same, the \(y\)-coordinate is negated). We also recall that reflections preserve distance and angle measure.

Part (a)

First, find the coordinates of \(L\). From the graph, \(L\) is at \((-3, 4)\)? Wait, no—wait, looking at the graph, \(L\) is at \((3, 4)\) (since it’s in the first quadrant, \(x = 3\), \(y = 4\)). Reflecting across the \(x\)-axis, \(L'\) should be \((3, -4)\). The statement says \(L'\) is at \((-3, 4)\), which is incorrect.

Answer:

False

Part (b)

Find \(M\)’s coordinates: \(M\) is at \((4, 1)\) (since it’s on the grid, \(x = 4\), \(y = 1\) above the \(x\)-axis). Reflecting across the \(x\)-axis, \(M'\) is \((4, -1)\), which is 1 unit below the \(x\)-axis.