Question

lets try: find the perimeter of δabc. round to the nearest tenth if necessary. a(-3, 5), b(4, 5), c(1, -4) grid image
lets try: find the perimeter of qrst. round to the nearest tenth if necessary. q(6, 0), r(-3, -5), s(-1, 4), t(2, 0) grid image
lets try: δjkl has a perimeter of 24 units. determine which ordered pair could be the coordinates of point k. select all that apply. (0, 2) □ (3, -4) □ (-3, 4) □ (5, 4) □ (-5, 2) □ (3, 5) □ grid image showing j and l

Explanation:

First Problem: Perimeter of \( \triangle ABC \) with \( A(-3, 5) \), \( B(4, 5) \), \( C(1, -4) \)

Step 1: Find \( AB \)

Since \( A \) and \( B \) have the same \( y \)-coordinate, \( AB \) is horizontal. The distance is \( |4 - (-3)| = 7 \).
\( AB = 7 \)

Step 2: Find \( AC \)

Use the distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). For \( A(-3, 5) \) and \( C(1, -4) \):
\( AC = \sqrt{(1 - (-3))^2 + (-4 - 5)^2} = \sqrt{4^2 + (-9)^2} = \sqrt{16 + 81} = \sqrt{97} \approx 9.8 \)

Step 3: Find \( BC \)

For \( B(4, 5) \) and \( C(1, -4) \):
\( BC = \sqrt{(1 - 4)^2 + (-4 - 5)^2} = \sqrt{(-3)^2 + (-9)^2} = \sqrt{9 + 81} = \sqrt{90} \approx 9.5 \)

Step 4: Perimeter

Perimeter \( = AB + AC + BC = 7 + 9.8 + 9.5 = 26.3 \)

Step 1: Find \( QR \)

Using distance formula: \( QR = \sqrt{(-3 - 6)^2 + (-5 - 0)^2} = \sqrt{(-9)^2 + (-5)^2} = \sqrt{81 + 25} = \sqrt{106} \approx 10.3 \)

Step 2: Find \( RS \)

\( RS = \sqrt{(-1 - (-3))^2 + (4 - (-5))^2} = \sqrt{2^2 + 9^2} = \sqrt{4 + 81} = \sqrt{85} \approx 9.2 \)

Step 3: Find \( ST \)

\( ST = \sqrt{(2 - (-1))^2 + (0 - 4)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \)

Step 4: Find \( TQ \)

\( TQ = \sqrt{(6 - 2)^2 + (0 - 0)^2} = \sqrt{4^2 + 0} = 4 \)

Step 5: Perimeter

Perimeter \( = QR + RS + ST + TQ \approx 10.3 + 9.2 + 5 + 4 = 28.5 \)

Answer:

\( 26.3 \)

Second Problem: Perimeter of \( QRST \) with \( Q(6, 0) \), \( R(-3, -5) \), \( S(-1, 4) \), \( T(2, 0) \)