Question

The coordinates of the vertices of △JKL are J(0, 2) , K(3, 1) , and L(1, −5) .

Drag and drop the choices into each box to correctly complete the sentences.

The slope of JK¯¯¯¯¯ is , the slope of KL¯¯¯¯¯ is , and the slope of JL¯¯¯¯¯ is . △JKL a right triangle because .

Answer 1

Answer: Look at the picture below for the answers :)

Explanation:

Answer 2

Part 1) The slope of JK is
`m_J_K=-(1)/(3)`

Part 2) The slope of KL is
`m_K_L=3`

Part 3) The slope of JL is
`m_J_L=-7`

Part 4) Triangle JKL is a right triangle because two of these slopes have a product of -1

Explanation:

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

`J(0, 2), K(3, 1),L(1, -5)`

Part 1) Find the slope JK

we have

`J(0, 2), K(3, 1)`

substitute in the formula

`m=(1-2)/(3-0)`

`m_J_K=-(1)/(3)`

Part 2) Find the slope KL

we have

`K(3, 1),L(1, -5)`

substitute in the formula

`m=(-5-1)/(1-3)`

`m_K_L=(-6)/(-2)`

`m_K_L=3`

Part 3) Find the slope JL

we have

`J(0, 2),L(1, -5)`

substitute in the formula

`m=(-5-2)/(1-0)`

`m_J_L=(-7)/(1)`

`m_J_L=-7`

Part 4) Compare the slopes

`m_J_K=-(1)/(3)`

`m_K_L=3`

`m_J_L=-7`

we have that

JK and KL are perpendicular because their slopes are opposite reciprocal

The product of their slopes is equal to -1

therefore

Triangle JKL is a right triangle because two of these slopes have a product of -1