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4×1+5
aw a ring around each of the calculations with a result that is a factor of 48
Point
P has coordinates
(k,-3).
Point
Q has coordinates
(2,-3).
The length of
PQ is 6.5 units and
k < 0
Find the value of
k.

k=

$4 \times 1+5$ $\newline$ aw a ring around each of the calculations with a result that is a factor of $48$ $\newline$ Point $P$ has coordinates $(k,-3)$ . $\newline$ Point $Q$ has coordinates $(2,-3)$ . $\newline$ The length of $P Q$ is $6$ . $5$ units and $k<0$ $\newline$ Find the value of $k$ . $\newline$ $k=$

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Write equations of cosine functions using properties

Full solution

Q.

4 \times 1+5

\newline

aw a ring around each of the calculations with a result that is a factor of

48

\newline

Point

P

has coordinates

(k,-3)

.

\newline

Point

Q

has coordinates

(2,-3)

.

\newline

The length of

P Q

is

6

.

5

units and

k<0

\newline

Find the value of

k

.

\newline

k=

Calculate Expression: $4\times1+5 = 4+5 = 9$ , which is not a factor of $48$ , so we don't circle it.
Find Distance Between Points: The distance between points $P(k, -3)$ and $Q(2, -3)$ is the absolute value of the difference in their $x$ -coordinates since they lie on the same horizontal line.
Calculate Length of PQ: The length of PQ is $|k - 2| = 6.5$ , since $k < 0$ , $k - 2$ must be negative, so we have $- (k - 2) = 6.5$ .
Solve for k: Solving for k, we get $-k + 2 = 6.5$ , so $k = 2 - 6.5$ .
Final Value of k: $k = -4.5$ , which is less than $0$ , so it fits the condition $k < 0$ .

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